Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-22T20:24:20.627Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  15 June 2023

Daniel Huybrechts
Affiliation:
Universität Bonn
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achter, Jeffrey. On the abelian fivefolds attached to cubic surfaces. Math. Res. Lett., 20(5):805824, 2013. (Cited on page 186.)Google Scholar
Addington, Nicolas. New derived symmetries of some hyperkähler varieties. Algebr. Geom., 3(2):223260, 2016. (Cited on pages 397 and 398.)Google Scholar
Addington, Nicolas. On two rationality conjectures for cubic fourfolds. Math. Res. Lett., 23(1):113, 2016. (Cited on pages 308, 340, 341, and 384.)Google Scholar
Addington, Nicolas and Auel, Asher. Some non-special cubic fourfolds. Doc. Math., 23:637651, 2018. (Cited on page 349.)Google Scholar
Addington, Nicolas and Giovenzana, Francesco. On the period of Lehn, Lehn, Sorger, and van Straten’s symplectic eightfold. arXiv:2003.10984. (Cited on page 342.)Google Scholar
Addington, Nicolas, Hassett, Brendan, Tschinkel, Yuri, and Várilly-Alvarado, Anthony. Cubic fourfolds fibered in sextic del Pezzo surfaces. Amer. J. Math., 141(6):14791500, 2019. (Cited on page 338.)Google Scholar
Addington, Nicolas and Lehn, Manfred. On the symplectic eightfold associated to a Pfaffian cubic fourfold. J. Reine Angew. Math., 731:129137, 2017. (Cited on pages 286, 342, 386, 389, and 397.)Google Scholar
Addington, Nicolas and Thomas, Richard. Hodge theory and derived categories of cubic fourfolds. Duke Math. J., 163(10):18851927, 2014. (Cited on pages 332, 339, 349, 377, 382, 385, and 392.)Google Scholar
Adler, Allan. Some integral representations of PSL2(Fp) and their applications. J. Algebra, 72(1):115145, 1981. (Cited on pages 216 and 244.)Google Scholar
Adler, Allan and Ramanan, S.. Moduli of abelian varieties, Vol. 1644 of Lecture Notes in Math. Berlin: Springer-Verlag, 1996. (Cited on page 245.)Google Scholar
Agostini, Daniele, Barros, Ignacio, and Lai, Kuan-Wen. On the irrationality of moduli spaces of K3 surfaces. arXiv:2011.11025. (Cited on page 148.)Google Scholar
Allcock, Daniel. The moduli space of cubic threefolds. J. Algebraic Geom., 12(2):201223, 2003. (Cited on page 243.)Google Scholar
Allcock, Daniel, Carlson, James, and Toledo, Domingo. The complex hyperbolic geometry of the moduli space of cubic surfaces. J. Algebraic Geom., 11(4):659724, 2002. (Cited on pages 74, 186, 187, 189, and 191.)Google Scholar
Allcock, Daniel, Carlson, James A., and Toledo, Domingo. The moduli space of cubic threefolds as a ball quotient. Mem. Amer. Math. Soc., 209(985):xii+70, 2011. (Cited on pages 74, 246, 247, and 248.)Google Scholar
Altman, Allen and Kleiman, Steven. Foundations of the theory of Fano schemes. Compositio Math., 34(1):347, 1977. (Cited on pages 75, 101, 103, 108, 113, 114, and 210.)Google Scholar
Aluffi, Paolo and Faber, Carel. Linear orbits of arbitrary plane curves. Michigan Math. J., 48(1):137, 2000. Dedicated to William Fulton on the occasion of his 60th birthday. (Cited on page 147.)Google Scholar
Amerik, Ekaterina. A computation of invariants of a rational self-map. Ann. Fac. Sci. Toulouse Math. (6), 18(3):445457, 2009. (Cited on pages 95, 312, 327, and 328.)Google Scholar
Amerik, Ekaterina and Voisin, Claire. Potential density of rational points on the variety of lines of a cubic fourfold. Duke Math. J., 145(2):379408, 2008. (Cited on pages 316 and 327.)Google Scholar
André, Yves. Mumford–Tate groups of mixed Hodge structures and the theorem of the fixed part. Compositio Math., 82(1):124, 1992. (Cited on page 26.)Google Scholar
André, Yves. Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Vol. 17 of Panoramas et Synthèses. Paris: Société Mathématique de France, 2004. (Cited on pages 4, 110, 112, 228, and 404.)Google Scholar
Andreotti, Aldo. On a theorem of Torelli. Amer. J. Math., 80:801828, 1958. (Cited on page 230.)Google Scholar
Anella, Fabrizio and Huybrechts, Daniel. Characteristic foliations. arXiv:2201.07624. (Cited on page 317.)Google Scholar
Arbarello, Enrico, Cornalba, Maurizio, Griffiths, Phillip, and Harris, Joe. Geometry of algebraic curves. Vol. I, Vol. 267 of Grundlehren der Mathematischen Wissenschaften. New York: Springer-Verlag, 1985. (Cited on pages 94, 96, 237, and 273.)Google Scholar
Artin, Michael and Mumford, David. Some elementary examples of unirational varieties which are not rational. Proc. London Math. Soc. (3), 25:7595, 1972. (Cited on page 88.)Google Scholar
Atiyah, Michael. Riemann surfaces and spin structures. Ann. Sci. École Norm. Sup. (4), 4(1):4762, 1971. (Cited on page 180.)Google Scholar
Atiyah, Michael and Hirzebruch, Friedrich. Vector bundles and homogeneous spaces. In Proc. Sympos. Pure Math., Vol. III, pp. 738. Providence, RI: American Mathematical Society, 1961. (Cited on page 383.)Google Scholar
Auel, Asher, Bernardara, Marcello, and Bolognesi, Michele. Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems. J. Math. Pures Appl. (9), 102(1):249291, 2014. (Cited on pages 63 and 260.)Google Scholar
Auel, Asher, Bernardara, Marcello, Bolognesi, Michele, and Várilly-Alvarado, Anthony. Cubic fourfolds containing a plane and a quintic del Pezzo surface. Algebr. Geom., 1(2):181193, 2014. (Cited on pages 257, 262, 338, and 349.)Google Scholar
Auslander, Maurice. Functors and morphisms determined by objects. In Representation theory of algebras (Proc. Conf., Temple Univ., Philadelphia, Pa., 1976), Vol. 37, pp. 1244. Lecture Notes in Pure Appl. Math., 1978. (Cited on pages 372 and 374.)Google Scholar
Badescu, Lucian. Algebraic surfaces. New York: Universitext, Springer-Verlag, 2001. Translated from the 1981 Romanian original by Vladimir Ma¸sek and revised by the author. (Cited on pages 161 and 164.)Google Scholar
Baily, Walter and Borel, Armand. Compactification of arithmetic quotients of bounded symmetric domains. Ann. of Math. (2), 84:442528, 1966. (Cited on page 343.)Google Scholar
Bakker, Benjamin, Brunebarbe, Yohan, and Tsimerman, Jacob. Quasiprojectivity of images of mixed period maps. arXiv:2006.13709. (Cited on page 152.)Google Scholar
Ballico, Edoardo, Catanese, Fabrizio, and Ciliberto, Ciro (eds.). Classification of irregular varieties, Vol. 1515 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1992. Minimal models and abelian varieties. (Cited on page 2.)Google Scholar
Banwait, Barinder, Fité, Francesc, and Loughran, Daniel. Del Pezzo surfaces over finite fields and their Frobenius traces. Math. Proc. Cambridge Philos. Soc., 167(1):3560, 2019. (Cited on pages 158, 159, and 160.)Google Scholar
Bardelli, Fabio. Polarized mixed Hodge structures: on irrationality of threefolds via degeneration. Ann. Mat. Pura Appl. (4), 137:287369, 1984. (Cited on page 239.)Google Scholar
Barth, Wolf. Counting singularities of quadratic forms on vector bundles. In Vector bundles and differential equations (Proc. Conf., Nice, 1979), Vol. 7 of Progr. Math., pp. 119. Boston, MA: Birkhäuser, 1980. (Cited on pages 62, 63, and 323.)Google Scholar
Barth, Wolf and Van de Ven, Antonius. Fano varieties of lines on hypersurfaces. Arch. Math. (Basel), 31(1):96104, 1978/79. (Cited on pages 75, 103, and 130.)Google Scholar
Bayer, Arend, Lahoz, Martí, Macrì, Emanuele, et al. Stability conditions in families. Publ. Math. Inst. Hautes Études Sci., 133:157325, 2021. (Cited on page 392.)Google Scholar
Bayer, Arend, Sjoerd, Beentjes, Feyzbakhsh, Soheyla, et al. The desingularization of the theta divisor of a cubic threefold as a moduli space. arXiv:2011.12240. (Cited on pages 221, 383, and 384.)Google Scholar
Beauville, Arnaud. Sur les hypersurfaces dont les sections hyperplanes sont à module constant. In The Grothendieck Festschrift, I, Vol. 86 of Progr. Math., pp. 121133. (Cited on pages 68 and 69.)Google Scholar
Beauville, Arnaud. Variétés de Prym et jacobiennes intermédiaires. Ann. Sci. École Norm. Sup. (4), 10(3):309391, 1977. (Cited on pages 61, 63, 193, 205, 221, and 228.)Google Scholar
Beauville, Arnaud. Les singularités du diviseur Θ de la jacobienne intermédiaire de l’hypersurface cubique dans ℙ4. In Algebraic threefolds (Varenna, 1981), Vol. 947 of Lecture Notes in Math., pp. 190208. Berlin, New York: Springer, 1982. (Cited on pages 193, 207, 225, 226, 232, 235, and 238.)Google Scholar
Beauville, Arnaud. Sous-variétés spéciales des variétés de Prym. Compositio Math., 45(3):357383, 1982. (Cited on pages 214, 220, 225, and 238.)Google Scholar
Beauville, Arnaud. Some remarks on Kähler manifolds with c1 = 0. In Classification of algebraic and analytic manifolds (Katata, 1982), Vol. 39 of Progr. Math., pp. 126. Boston, MA: Birkhäuser 1983. (Cited on page 296.)Google Scholar
Beauville, Arnaud. Variétés Kähleriennes dont la première classe de Chern est nulle. J. differential Geom., 18(4):755782 (1984), 1983. (Cited on pages 292, 293, and 294.)Google Scholar
Beauville, Arnaud. Le groupe de monodromie des familles universelles d’hypersurfaces et d’intersections complètes. In Complex analysis and algebraic geometry (Göttingen, 1985), Vol. 1194 of Lecture Notes in Math., pp. 818. Berlin: Springer, 1986. (Cited on pages 23, 28, 29, and 30.)Google Scholar
Beauville, Arnaud. Le problème de Torelli. Number 145–146, pages 3, 720. 1987. Séminaire Bourbaki, Vol. 1985/86. (Cited on pages 148 and 154.)Google Scholar
Beauville, Arnaud. Prym varieties: a survey. In Theta functions–Bowdoin 1987, Part 1 (Brunswick, ME, 1987), Vol. 49 of Proc. Sympos. Pure Math., pp. 607620. Providence, RI: Amer. Math. Soc., 1989. (Cited on page 221.)Google Scholar
Beauville, Arnaud. Complex algebraic surfaces, Vol. 34 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2nd ed., 1996. Translated from the 1978 French original by R. Barlow, with assistance from N. I. Shepherd-Barron and M. Reid. (Cited on pages 156, 164, 167, and 178.)Google Scholar
Beauville, Arnaud. Determinantal hypersurfaces. Michigan Math. J., 48:3964, 2000. Dedicated to William Fulton on the occasion of his 60th birthday. (Cited on pages 173, 245, 276, and 289.)Google Scholar
Beauville, Arnaud. Vector bundles on the cubic threefold. In Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000), Vol. 312 of Contemp. Math., pp. 7186. Providence, RI: Amer. Math. Soc., 2002. (Cited on pages 220 and 270.)Google Scholar
Beauville, Arnaud. On the splitting of the Bloch–Beilinson filtration. In Algebraic cycles and motives. Vol. 2, Vol. 344 of London Math. Soc. Lecture Note Ser., pp. 3853. Cambridge: Cambridge University Press, 2007. (Cited on page 401.)Google Scholar
Beauville, Arnaud. Moduli of cubic surfaces and Hodge theory (after Allcock, Carlson, Toledo). In Géométries à courbure négative ou nulle, groupes discrets et rigidités, Vol. 18 of Sémin. Congr., pp. 445466. Paris: Soc. Math. France, 2009. (Cited on pages 186, 187, 188, 189, and 191.)Google Scholar
Beauville, Arnaud. The primitive cohomology lattice of a complete intersection. C. R. Math. Acad. Sci. Paris, 347(23–24):13991402, 2009. (Cited on page 13.)Google Scholar
Beauville, Arnaud. Some surfaces with maximal Picard number. J. Éc. polytech. Math., 1:101116, 2014. (Cited on pages 216 and 244.)Google Scholar
Beauville, Arnaud. The Lüroth problem. In Rationality problems in algebraic geometry, Vol. 2172 of Lecture Notes in Math., pp. 127. Cham: Springer, 2016. (Cited on pages 237, 238, 239, and 244.)Google Scholar
Beauville, Arnaud. Vector bundles on Fano threefolds and K3 surfaces. Boll. Unione Mat. Ital., 15(1–2):4355, 2022. (Cited on pages 220 and 270.)Google Scholar
Beauville, Arnaud and Donagi, Ron. La variété des droites d’une hypersurface cubique de dimension 4. C. R. Acad. Sci. Paris Sér. I Math., 301(14):703706, 1985. (Cited on pages 122, 127, 251, 273, 275, 280, 288, 296, and 301.)Google Scholar
Beauville, Arnaud and Voisin, Claire. On the Chow ring of a K3 surface. J. Algebraic Geom., 13(3):417426, 2004. (Cited on page 401.)Google Scholar
Beheshti, Roya. Lines on projective hypersurfaces. J. Reine Angew. Math., 592:121, 2006. (Cited on page 89.)Google Scholar
Beklemishev, Nikolay. Invariants of cubic forms of four variables. Vestnik Moskov. Univ. Ser. I Mat. Mekh., (2):4249, 116, 1982. (Cited on pages 183 and 185.)Google Scholar
Belmans, Pieter, Fu, Lie, and Raedschelders, Theo. Derived categories of flips and cubic hypersurfaces. arXiv:2002.04940. (Cited on pages 110, 375, and 376.)Google Scholar
Benoist, Olivier. Séparation et propriété de Deligne–Mumford des champs de modules d’intersections complètes lisses. J. Lond. Math. Soc. (2), 87(1):138156, 2013. (Cited on page 38.)Google Scholar
Bernardara, Marcello. A semiorthogonal decomposition for Brauer–Severi schemes. Math. Nachr., 282(10):14061413, 2009. (Cited on page 355.)Google Scholar
Bernardara, Marcello, Macrì, Emanuele, Mehrotra, Sukhendu, and Stellari, Paolo. A categorical invariant for cubic threefolds. Adv. Math., 229(2):770803, 2012. (Cited on pages 377, 378, 380, 381, 382, and 383.)Google Scholar
Bernardara, Marcello and Tabuada, Gonçalo. From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives. Mosc. Math. J., 16(2):205235, 2016. (Cited on page 383.)Google Scholar
Betten, Anton and Karaoglu, Fatmas. The Eckardt point configuration of cubic surfaces revisited. Des. Codes Cryptogr., 90:21592180, 2022. (Cited on page 182.)Google Scholar
Bini, Gilberto and Garbagnati, Alice. Quotients of the Dwork pencil. J. Geom. Phys., 75:173198, 2014. (Cited on page 22.)Google Scholar
Biswas, Indranil, Biswas, Jishnu, and Ravindra, G. Ṽ.. On some moduli spaces of stable vector bundles on cubic and quartic threefolds. J. Pure Appl. Algebra, 212(10):22982306, 2008. (Cited on page 220.)Google Scholar
Bittner, Franziska. The universal Euler characteristic for varieties of characteristic zero. Compositio Math., 140(4):10111032, 2004. (Cited on pages 113, 114, and 116.)Google Scholar
Bloch, Spencer. Lectures on algebraic cycles. Duke University Mathematics Series, IV. Durham, NC: Duke University Mathematics Department, 1980. (Cited on page 228.)Google Scholar
Bloch, Spencer and Srinivas, Vasudevan. Remarks on correspondences and algebraic cycles. Amer. J. Math., 105(5):12351253, 1983. (Cited on pages 228, 254, 400, and 402.)Google Scholar
Bockondas, Gloire Grace and Boissière, Samuel. Triple lines on a cubic threefold. arXiv:2201.08884. (Cited on page 198.)Google Scholar
Bogomolov, Fjodor. On the cohomology ring of a simple hyper-Kähler manifold (on the results of Verbitsky). Geom. Funct. Anal., 6(4):612618, 1996. (Cited on page 297.)Google Scholar
Böhning, Christian and Graf von Bothmer, Hans-Christian. Matrix factorizations and intermediate Jacobians of cubic threefolds. arXiv:2112.10554. (Cited on page 220.)Google Scholar
Boissière, Samuel, Camere, Chiara, and Sarti, Alessandra. Cubic threefolds and hyperkähler manifolds uniformized by the 10-dimensional complex ball. Math. Ann., 373(3–4):14291455, 2019. (Cited on pages 246 and 249.)Google Scholar
Boissière, Samuel, Nieper-Wißkirchen, Marc, and Sarti, Alessandra. Smith theory and irreducible holomorphic symplectic manifolds. J. Topol., 6(2):361390, 2013. (Cited on pages 294 and 303.)Google Scholar
Bolognesi, Michele and Pedrini, Claudio. The transcendental motive of a cubic fourfold. J. Pure Appl. Algebra, 224(8):106333, 16, 2020. (Cited on page 306.)Google Scholar
Bolognesi, Michele, Russo, Francesco, and Staglianò, Giovanni. Some loci of rational cubic fourfolds. Math. Ann., 373(1–2):165190, 2019. (Cited on pages 288 and 337.)Google Scholar
Bombieri, Enrico and Swinnerton-Dyer, Peter. On the local zeta function of a cubic threefold. Ann. Scuola Norm. Sup. Pisa (3), 21:129, 1967. (Cited on pages 16, 61, 113, 193, 205, and 221.)Google Scholar
Bondal, Alexei and Kapranov, Mikhai. Representable functors, Serre functors, and reconstructions. Izv. Akad. Nauk SSSR Ser. Mat., 53(6):11831205, 1337, 1989. (Cited on pages 359 and 361.)Google Scholar
Bondal, Alexei and Orlov, Dmitri. Reconstruction of a variety from the derived category and groups of autoequivalences. Compositio Math., 125(3):327344, 2001. (Cited on page 356.)Google Scholar
Bondal, Alexei and Van den Bergh, Michel. Generators and representability of functors in commutative and noncommutative geometry. Mosc. Math. J., 3(1):136, 258, 2003. (Cited on page 356.)Google Scholar
Bondal, Alexey, Larsen, Michael, and Lunts, Valery. Grothendieck ring of pretriangulated categories. Int. Math. Res. Not., (29):1461–1495, 2004. (Cited on page 375.)Google Scholar
Borcea, Ciprian. Deforming varieties of k-planes of projective complete intersections. Pacific J. Math., 143(1):2536, 1990. (Cited on pages 103 and 109.)Google Scholar
Borel, Armand. Sur l’homologie et la cohomologie des groupes de Lie compacts connexes. Amer. J. Math., 76:273342, 1954. (Cited on page 144.)Google Scholar
Borel, Armand. Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem. J. differential Geometry, 6:543560, 1972. Collection of articles dedicated to S. S. Chern and D. C. Spencer on their 60th birthdays. (Cited on page 343.)Google Scholar
Borisov, Lev and Căldăraru, Andrei. The Pfaffian–Grassmannian derived equivalence. J. Algebraic Geom., 18(2):201222, 2009. (Cited on page 274.)Google Scholar
Borisov, Lev and Libgober, Anatoly. Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex. In Mirror symmetry, IV (Montreal, QC, 2000), Vol. 33 of AMS/IP Stud. Adv. Math., pp. 325342. Providence, RI: Amer. Math. Soc., 2002. (Cited on page 121.)Google Scholar
Bourbaki, Nicolas. Algebra. II. Chapters 4–7. Elements of Mathematics. Berlin: Springer-Verlag, 1990. Translated from the French by P. M. Cohn and J. Howie. (Cited on page 18.)Google Scholar
Brakkee, Emma. Two polarised K3 surfaces associated to the same cubic fourfold. Math. Proc. Cambridge Philos. Soc., 171(1):5164, 2021. (Cited on pages 336, 345, and 352.)Google Scholar
Bricalli, Davide, Favale, Filippo, and Pirola, Gian Pietro. A theorem of Gordan and Noether via Gorenstein rings. arXiv:2201.07550. (Cited on page 46.)Google Scholar
Brion, Michel. Equivariant cohomology and equivariant intersection theory. In Representation theories and algebraic geometry (Montreal, PQ, 1997), volume 514 of NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., pp. 137. Dordrecht Kluwer Acad. Publ., 1998. Notes by Alvaro Rittatore. (Cited on page 145.)Google Scholar
Browder, William. Surgery on simply-connected manifolds. New York, Heidelberg: Springer-Verlag, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65. (Cited on page 24.)Google Scholar
Browder, William. Complete intersections and the Kervaire invariant. In Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978), Vol. 763 of Lecture Notes in Math., pp. 88108. Berlin: Springer, 1979. (Cited on page 24.)Google Scholar
Brown, Gavin and Ryder, Daniel. Elliptic fibrations on cubic surfaces. J. Pure Appl. Algebra, 214(4):410421, 2010. (Cited on page 172.)Google Scholar
Buchweitz, Ragnar-Olaf. Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings. https://tspace.library.utoronto.ca/handle/1807/16682, 1986. (Cited on pages 371 and 373.)Google Scholar
Buckley, Anita and Košir, Tomaž. Determinantal representations of smooth cubic surfaces. Geom. Dedicata, 125:115140, 2007. (Cited on page 173.)Google Scholar
Bülles, Tim-Henrik. Motives of moduli spaces on K3 surfaces and of special cubic four-folds. Manuscripta Math., 161(1–2):109124, 2020. (Cited on pages 306 and 406.)Google Scholar
Bunnett, Dominic and Keneshlou, Hanieh. Determinantal representations of the cubic discriminant. Matematiche (Catania), 75(2):489505, 2020. (Cited on page 21.)Google Scholar
Busé, Laurent and Jouanolou, Jean-Pierre. On the discriminant scheme of homogeneous polynomials. Math. Comput. Sci., 8(2):175234, 2014. (Cited on page 20.)Google Scholar
Canonaco, Alberto and Stellari, Paolo. Twisted Fourier–Mukai functors. Adv. Math., 212(2):484503, 2007. (Cited on page 356.)Google Scholar
Carlson, James and Griffiths, Phillip. Infinitesimal variations of Hodge structure and the global Torelli problem. In Journées de Géometrie Algébrique d’Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, pp. 5176. Alphen aan den Rijn: Sijthoff & Noordhoff, 1980. (Cited on pages 52 and 154.)Google Scholar
Carlson, James, Müller-Stach, Stefan, and Peters, Chris. Period mappings and period domains, Vol. 85 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2nd ed., 2017. (Cited on pages 52, 57, 149, and 154.)Google Scholar
Carlson, James A. and Toledo, Domingo. Compact quotients of non-classical domains are not Kähler. In Hodge theory, complex geometry, and representation theory, Vol. 608 of Contemp. Math., pp. 5157. Providence, RI: Amer. Math. Soc., 2014. (Cited on page 151.)Google Scholar
Casalaina-Martin, Sebastian and Friedman, Robert. Cubic threefolds and abelian varieties of dimension five. J. Algebraic Geom., 14(2):295326, 2005. (Cited on page 235.)Google Scholar
Casalaina-Martin, Sebastian, Grushevsky, Samuel, Hulek, Klaus, and Laza, Radu. Non-isomorphic smooth compactifications of the moduli space of cubic surfaces. arXiv:2207.03533. (Cited on page 191.)Google Scholar
Casalaina-Martin, Sebastian, Grushevsky, Samuel, Hulek, Klaus, and Laza, Radu. Complete moduli of cubic threefolds and their intermediate Jacobians. Proc. Lond. Math. Soc. (3), 122(2):259316, 2021. (Cited on page 244.)Google Scholar
Casalaina-Martin, Sebastian and Laza, Radu. The moduli space of cubic threefolds via degenerations of the intermediate Jacobian. J. Reine Angew. Math., 633:2965, 2009. (Cited on page 244.)Google Scholar
Casalaina-Martin, Sebastian, Popa, Mihnea, and Schreieder, Stefan. Generic vanishing and minimal cohomology classes on abelian fivefolds. J. Algebraic Geom., 27(3):553581, 2018. (Cited on page 227.)Google Scholar
Cayley, Arthur. On the triple tangent planes of surfaces of the third order. Cambridge and Dublin Math. Journal, IV:118132, 1849. (Cited on page 175.)Google Scholar
Cayley, Arthur. A memoir on cubic surfaces. Philos. Trans. R. Soc. Lond., 159:231326, 1869. (Cited on page 183.)Google Scholar
Chambert-Loir, Antoine, Nicaise, Johannes, and Sebag, Julien. Motivic integration, Vol. 325 of Progress in Mathematics. New York: Birkhäuser/Springer, 2018. (Cited on pages 110 and 111.)Google Scholar
Charles, François. A remark on the Torelli theorem for cubic fourfolds. arXiv:1209.4509. (Cited on pages 107, 292, 300, 347, and 383.)Google Scholar
Chen, Xi, Pan, Xuanyu, and Zhang, Dingxin. Automorphism and cohomology II: complete intersections. arXiv:1511.07906. (Cited on pages 38 and 39.)Google Scholar
Chow, Wei-Liang. On the geometry of algebraic homogeneous spaces. Ann. of Math. (2), 50:3267, 1949. (Cited on page 108.)Google Scholar
Clebsch, Alfred. Ueber die Anwendung der quadratischen Substitution auf die Gleichungen 5 ten Grades und die geometrische Theorie des ebenen Fünfseits. Math. Ann., 4(2):284345, 1871. (Cited on page 173.)Google Scholar
Clebsch, Alfred. On Weiler’s models. Gött. Nachr., 1872:402403, 1872. (Cited on page 183.)Google Scholar
Clemens, Herbert and Griffiths, Phillip. The intermediate Jacobian of the cubic threefold. Ann. of Math. (2), 95:281356, 1972. (Cited on pages 94, 104, 127, 193, 197, 198, 200, 202, 209, 210, 212, 215, 225, 229, 230, 234, 237, 238, and 240.)Google Scholar
Collino, Alberto. A cheap proof of the irrationality of most cubic threefolds. Boll. Un. Mat. Ital. B (5), 16(2):451465, 1979. (Cited on page 239.)Google Scholar
Collino, Alberto. The fundamental group of the Fano surface. I, II. In Algebraic threefolds (Varenna, 1981), Vol. 947 of Lecture Notes in Math., pp. 209218, 219–220. Berlin, New York: Springer, 1982. (Cited on pages 203 and 204.)Google Scholar
Collino, Alberto, Naranjo, Juan Carlos, and Pirola, Gian Pietro. The Fano normal function. J. Math. Pures Appl. (9), 98(3):346366, 2012. (Cited on page 228.)Google Scholar
Colombo, Elisabetta and van Geemen, Bert. The Chow group of the moduli space of marked cubic surfaces. Ann. Mat. Pura Appl. (4), 183(3):291316, 2004. (Cited on page 185.)Google Scholar
Comaschi, Gaia. Pfaffian representations of cubic threefolds. arXiv:2005.06593. (Cited on page 245.)Google Scholar
Coskun, Izzet and Starr, Jason. Rational curves on smooth cubic hypersurfaces. Int. Math. Res. Not. IMRN, (24):4626–4641, 2009. (Cited on pages 104, 198, and 253.)Google Scholar
Cox, David. Generic Torelli and infinitesimal variation of Hodge structure. In Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Vol. 46 of Proc. Sympos. Pure Math., pp. 235246. Providence, RI: Amer. Math. Soc., 1987. (Cited on page 49.)Google Scholar
Cox, David, Little, John, and O’Shea, Donal. Using algebraic geometry, Vol. 185 of Graduate Texts in Mathematics. New York: Springer, 2005. (Cited on pages 20 and 21.)Google Scholar
Coxeter, Harold. The polytopes with regular-prismatic vertex figures. Proc. London Math. Soc. (2), 34(2):126189, 1932. (Cited on page 179.)Google Scholar
Coxeter, Harold. Extreme forms. Canadian J. Math., 3:391441, 1951. (Cited on page 163.)Google Scholar
Coxeter, Harold. The twenty-seven lines on the cubic surface. In Convexity and its applications, pp. 111119. Basel: Birkhäuser, 1983. (Cited on page 175.)Google Scholar
Cukierman, Fernando. Families of Weierstrass points. Duke Math. J., 58(2):317346, 1989. (Cited on page 180.)Google Scholar
Dardanelli, Elisa and van Geemen, Bert. Hessians and the moduli space of cubic surfaces. In Algebraic geometry, Vol. 422 of Contemp. Math., pp. 1736. Providence, RI: Amer. Math. Soc., 2007. (Cited on pages 184 and 185.)Google Scholar
Das, Ronno. Cohomology of the universal smooth cubic surface. Q. J. Math., 72(3):795815, 2021. (Cited on pages 146 and 159.)Google Scholar
Das, Ronno. The space of cubic surfaces equipped with a line. Math. Z., 298(1–2):653670, 2021. (Cited on page 146.)Google Scholar
de Jong, Johan and Starr, Jason. Cubic fourfolds and spaces of rational curves. Illinois J. Math., 48(2):415450, 2004. (Cited on page 299.)Google Scholar
Debarre, Olivier. Hyperkähler manifolds. arXiv:1810.02087. (Cited on page 348.)Google Scholar
Debarre, Olivier. Minimal cohomology classes and Jacobians. J. Algebraic Geom., 4(2):321335, 1995. (Cited on page 227.)Google Scholar
Debarre, Olivier. Higher-dimensional algebraic geometry. New York: Universitext, Springer-Verlag, 2001. (Cited on page 122.)Google Scholar
Debarre, Olivier. Variétés rationnellement connexes (d’après T. Graber, J. Harris, J. Starr, et A. J. de Jong). Astérisque, (290):Exp. No. 905, ix, 243266, 2003. Séminaire Bourbaki. Vol. 2001/2002. (Cited on page 122.)Google Scholar
Debarre, Olivier, Laface, Antonio, and Roulleau, Xavier. Lines on cubic hypersurfaces over finite fields. In Geometry over nonclosed fields, Simons Symp., pp. 1951. Cham: Springer, 2017. (Cited on pages 124 and 217.)Google Scholar
Debarre, Olivier and Manivel, Laurent. Sur la variété des espaces linéaires contenus dans une intersection complète. Math. Ann., 312(3):549574, 1998. (Cited on pages 107 and 121.)Google Scholar
Degtyarev, Alex. Smooth models of singular K3-surfaces. Rev. Mat. Iberoam., 35(1):125172, 2019. (Cited on page 47.)Google Scholar
Degtyarev, Alex, Itenberg, Ilia, and Ottem, John. Planes in cubic fourfolds. arXiv:2105.13951. (Cited on page 256.)Google Scholar
Deligne, Pierre. Travaux de Griffiths. In Séminaire Bourbaki, 22ème année (1969/70), Exp. No. 376, Vol. 180, pp. 213237. Lecture Notes in Math. Berlin: Springer, 1971. (Cited on page 148.)Google Scholar
Deligne, Pierre. La conjecture de Weil pour les surfaces K3. Invent. Math., 15:206226, 1972. (Cited on page 26.)Google Scholar
Deligne, Pierre. La conjecture de Weil. II. Inst. Hautes Études Sci. Publ. Math., (52):137–252, 1980. (Cited on pages 1, 25, and 28.)Google Scholar
Deligne, Pierre and Illusie, Luc. Relèvements modulo p2 et décomposition du complexe de de Rham. Invent. Math., 89(2):247270, 1987. (Cited on pages 15, 53, 54, and 103.)Google Scholar
Deligne, Pierre and Katz, Nicholas. Groupes de monodromie en géométrie algébrique (Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II)), Vol. 340 of Lecture Notes in Math. Berlin, New York: Springer, 1973. (Cited on pages 1, 9, 19, 21, and 71.)Google Scholar
Demailly, Jean-Pierre. Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials. In Algebraic geometry–Santa Cruz 1995, Vol. 62 of Proc. Sympos. Pure Math., pp. 285360. Providence, RI: Amer. Math. Soc., 1997. (Cited on page 214.)Google Scholar
Demazure, Michel. Résultant, discriminant. Enseign. Math. (2), 58(3–4):333373, 2012. (Cited on page 20.)Google Scholar
Diamond, Benjamin. Smooth surfaces in smooth fourfolds with vanishing first Chern class. J. Pure Appl. Algebra, 222(5):11641188, 2018. (Cited on page 102.)Google Scholar
Diaz, Humberto Anthony. The motive of the Fano surface of lines. C. R. Math. Acad. Sci. Paris, 354(9):925930, 2016. (Cited on pages 228 and 404.)Google Scholar
Diaz, Humberto Anthony. The Chow ring of a cubic hypersurface. Int. Math. Res. Not. IMRN, (22):17071–17090, 2021. (Cited on pages 5, 113, 400, and 403.)Google Scholar
Diaz, Steven and Harbater, David. Strong Bertini theorems. Trans. Amer. Math. Soc., 324(1):7386, 1991. (Cited on page 168.)Google Scholar
Dieudonné, Jean. Éléments d’analyse. Tome IX. Chapitre XXIV. Cahiers Scientifiques, XL11. Paris: Gauthier-Villars, 1982. (Cited on pages 2 and 204.)Google Scholar
Dimca, Alexandru, Gondim, Rodrigo, and Ilardi, Giovanna. Higher order Jacobians, Hessians and Milnor algebras. Collect. Math., 71(3):407425, 2020. (Cited on page 46.)Google Scholar
Dolgachev, Igor. Lectures on invariant theory, Vol. 296 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 2003. (Cited on pages 135, 147, 185, and 201.)Google Scholar
Dolgachev, Igor. Classical algebraic geometry. Cambridge: Cambridge University Press, 2012. A modern view. (Cited on pages 40, 68, 70, 156, 170, 173, 174, 175, 177, 179, 182, 184, 245, 286, and 289.)Google Scholar
Dolgachev, Igor. Corrado Segre and nodal cubic threefolds. In From classical to modern algebraic geometry, Trends Hist. Sci., pp. 429450. Cham: Birkhäuser/Springer, 2016. (Cited on page 245.)Google Scholar
Dolgachev, Igor, van Geemen, Bert, and Kondō, Shigeyuki. A complex ball uniformization of the moduli space of cubic surfaces via periods of K3 surfaces. J. Reine Angew. Math., 588:99148, 2005. (Cited on pages 171, 172, 186, 192, and 263.)Google Scholar
Donagi, Ron. Generic Torelli for projective hypersurfaces. Compositio Math., 50(2–3):325353, 1983. (Cited on pages 46, 47, 49, 50, and 154.)Google Scholar
Donagi, Ron and Green, Mark. A new proof of the symmetrizer lemma and a stronger weak Torelli theorem for projective hypersurfaces. J. differential Geom., 20(2):459461, 1984. (Cited on pages 49 and 50.)Google Scholar
Donagi, Ron and Markman, Eyal. Spectral covers, algebraically completely integrable, Hamiltonian systems, and moduli of bundles. In Integrable systems and quantum groups (Montecatini Terme, 1993), Vol. 1620 of Lecture Notes in Math., pp. 1119. Berlin: Springer, 1996. (Cited on page 298.)Google Scholar
Donagi, Ron and Smith, Roy Campbell. The structure of the Prym map. Acta Math., 146(1–2):25102, 1981. (Cited on page 222.)Google Scholar
Druel, Stéphane. Espace des modules des faisceaux de rang 2 semi-stables de classes de Chern c1 = 0, c2 = 2 et c3 = 0 sur la cubique de ℙ4. Internat. Math. Res. Notices, (19):985–1004, 2000. (Cited on page 220.)Google Scholar
Dwork, Bernard. On the zeta function of a hypersurface. Inst. Hautes Études Sci. Publ. Math., (12):5–68, 1962. (Cited on page 16.)Google Scholar
Dyckerhoff, Tobias and Murfet, Daniel. The Kapustin–Li formula revisited. Adv. Math., 231(3-4):18581885, 2012. (Cited on pages 372 and 374.)Google Scholar
Ebeling, Wolfgang. An arithmetic characterisation of the symmetric monodromy groups of singularities. Invent. Math., 77(1):8599, 1984. (Cited on page 29.)Google Scholar
Eckardt, Friedrich. Ueber diejenigen Flächen dritten Grades, auf denen sich drei gerade Linien in einem Punkte schneiden. Math. Ann., 10(2):227272, 1876. (Cited on page 182.)Google Scholar
Edge, William. Cubic primals in [4] with polar heptahedra. Proc. Roy. Soc. Edinburgh Sect. A, 77(1–2):151162, 1977. (Cited on page 246.)Google Scholar
Edge, William. The discriminant of a cubic surface. Proc. Roy. Irish Acad. Sect. A, 80(1):7578, 1980. (Cited on pages 21 and 184.)Google Scholar
Efimov, Alexander. Some remarks on L-equivalence of algebraic varieties. Selecta Math. (N.S.), 24(4):37533762, 2018. (Cited on page 116.)Google Scholar
Eisenbud, David. Homological algebra on a complete intersection, with an application to group representations. Trans. Amer. Math. Soc., 260(1):3564, 1980. (Cited on page 373.)Google Scholar
Eisenbud, David and Harris, Joe. 3264 and all that–a second course in algebraic geometry. Cambridge: Cambridge University Press, 2016. (Cited on pages 70, 71, 75, 89, 93, 94, 96, 275, 283, and 312.)Google Scholar
Esnault, Hélène, Levine, Marc, and Viehweg, Eckart. Chow groups of projective varieties of very small degree. Duke Math. J., 87(1):2958, 1997. (Cited on page 400.)Google Scholar
Fan, Yu-Wei and Lai, Kuan-Wen. New rational cubic fourfolds arising from Cremona transformations. arXiv:2003.00366. (Cited on page 395.)Google Scholar
Fano, Gino. Sul sistema ∞2 di rette contenuto in una varietà cubica generale dello spazio a quattro dimensioni. Math. Ann., 39(1–2):778792, 1904. (Cited on pages 193, 288, and 323.)Google Scholar
Fantechi, Barbara, Göttsche, Lothar, Illusie, Luc, et al. Fundamental algebraic geometry, Vol. 123 of Mathematical Surveys and Monographs. Providence, RI: Amer. Math. Soc., 2005. Grothendieck’s FGA explained. (Cited on pages 33, 34, 35, 36, 76, 81, and 82.)Google Scholar
Farkas, Gavril. Prym varieties and their moduli. In Contributions to algebraic geometry, EMS Ser. Congr. Rep., pp. 215255. Zürich: Eur. Math. Soc., 2012. (Cited on page 221.)Google Scholar
Farkas, Gavril and Verra, Alessandro. The universal K3 surface of genus 14 via cubic fourfolds. J. Math. Pures Appl. (9), 111:120, 2018. (Cited on page 335.)Google Scholar
Fedorchuk, Maksym. GIT semistability of Hilbert points of Milnor algebras. Math. Ann., 367(1–2):441460, 2017. (Cited on page 139.)Google Scholar
Fu, Lie. Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfolds. Glasg. Math. J., 58(1):1737, 2016. (Cited on page 40.)Google Scholar
Fu, Lie, Laterveer, Robert, and Vial, Charles. The generalized Franchetta conjecture for some hyper-Kähler varieties, II. J. Éc. polytech. Math., 8:10651097, 2021. (Cited on pages 113 and 306.)Google Scholar
Fu, Lie, Laterveer, Robert, and Vial, Charles. Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type. Ann. Mat. Pura Appl. (4), 200(5):20852126, 2021. (Cited on pages 5 and 403.)Google Scholar
Fu, Lie and Tian, Zhiyn. 2-cycles sur les hypersurfaces cubiques de dimension 5. Math. Z., 293(1–2):661676, 2019. (Cited on page 400.)Google Scholar
Fu, Lie and Vial, Charles. Cubic fourfolds, Kuznetsov components and Chow motives. arXiv:2009.13173. (Cited on page 406.)Google Scholar
Fujiki, Akira. On the de Rham cohomology group of a compact Kähler symplectic manifold. In Algebraic geometry, Sendai, 1985, Vol. 10 of Adv. Stud. Pure Math., pp. 105165. Amsterdam: North-Holland, 1987. (Cited on page 294.)Google Scholar
Fulton, William. Intersection theory, Vol. 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. Berlin: Springer-Verlag, 2nd ed., 1998. (Cited on pages 235, 283, and 312.)Google Scholar
Fulton, William and Lazarsfeld, Robert. On the connectedness of degeneracy loci and special divisors. Acta Math., 146(3–4):271283, 1981. (Cited on pages 94 and 283.)Google Scholar
Galkin, Sergey and Shinder, Evgeny. The Fano variety of lines and rationality problem for a cubic hypersurface. arXiv:1405.5154. (Cited on pages 110, 111, 113, 118, 123, 124, 239, 242, 271, 341, and 384.)Google Scholar
Galkin, Sergey and Shinder, Evgeny. On a zeta-function of a dgcategory. arXiv:1506.05831. (Cited on page 399.)Google Scholar
Ganter, Nora and Kapranov, Mikhail. Symmetric and exterior powers of categories. Transform. Groups, 19(1):57103, 2014. (Cited on page 398.)Google Scholar
Gelfand, Israel M., Kapranov, Mikhail, and Zelevinsky, Andrei. Discriminants, resultants and multidimensional determinants. Modern Birkhäuser Classics. Boston, MA: Birkhäuser Boston, Inc., 2008. Reprint of the 1994 ed. (Cited on pages 20 and 233.)Google Scholar
Gelfand, Sergei and Manin, Yuri. Methods of homological algebra. Springer Monographs in Mathematics. Berllin: Springer-Verlag, 2nd ed. 2003. (Cited on pages 356 and 382.)Google Scholar
González-Aguilera, Víctor and Liendo, Alvaro. Automorphisms of prime order of smooth cubic n-folds. Arch. Math. (Basel), 97(1):2537, 2011. (Cited on page 40.)Google Scholar
González-Aguilera, Víctor and Liendo, Alvaro. On the order of an automorphism of a smooth hypersurface. Israel J. Math., 197(1):2949, 2013. (Cited on pages 32 and 40.)Google Scholar
Goodman, Roe and Wallach, Nolan. Symmetry, representations, and invariants, Vol. 255 of Graduate Texts in Mathematics. Dordrecht: Springer, 2009. (Cited on page 26.)Google Scholar
Görtz, Ulrich and Wedhorn, Torsten. Algebraic geometry I. Advanced Lectures in Mathematics. Vieweg + Teubner, Wiesbaden, 2010. Schemes with examples and exercises. (Cited on page 108.)Google Scholar
Goryunov, Victor. Symmetric quartics with many nodes. In Singularities and bifurcations, Vol. 21 of Adv. Soviet Math., pp. 147161. Providence, RI: Amer. Math. Soc., 1994. (Cited on page 68.)Google Scholar
Gounelas, Frank and Kouvidakis, Alexis. Geometry of lines on a cubic fourfold. arXiv:2109.08493. (Cited on pages 97 and 315.)Google Scholar
Gounelas, Frank and Kouvidakis, Alexis. On some invariants of cubic fourfolds. arXiv:2008.05162. (Cited on pages 318 and 320.)Google Scholar
Gounelas, Frank and Kouvidakis, Alexis. Measures of irrationality of the Fano surface of a cubic threefold. Trans. Amer. Math. Soc., 371(10):71117133, 2019. (Cited on pages 207, 244, and 245.)Google Scholar
Griffiths, Phillip. Hermitian differential geometry, Chern classes, and positive vector bundles. In Global Analysis (Papers in Honor of K. Kodaira), pp. 185251. Tokyo: University of Tokyo Press, 1969. (Cited on page 319.)Google Scholar
Griffiths, Phillip, editor. Topics in transcendental algebraic geometry, Vol. 106 of Annals of Mathematics Studies, Princeton, NJ: Princeton University Press, 1984. (Cited on pages 148 and 149.)Google Scholar
Griffiths, Phillip and Harris, Joseph. Principles of algebraic geometry. New York: Wiley-Interscience [John Wiley & Sons], 1978. Pure and Applied Mathematics. (Cited on pages 45, 80, and 271.)Google Scholar
Griffiths, Phillip, Robles, Colleen, and Toledo, Domingo. Quotients of non-classical flag domains are not algebraic. Algebr. Geom., 1(1):113, 2014. (Cited on page 151.)Google Scholar
Gross, Mark, Huybrechts, Daniel, and Joyce, Dominic. Calabi–Yau manifolds and related geometries. Berlin: Universitext, Springer-Verlag, 2003. Lectures from the Summer School held in Nordfjordeid, June 2001. (Cited on pages 294 and 315.)Google Scholar
Gross, Mark and Popescu, Sorin. The moduli space of (1, 11)-polarized abelian surfaces is unirational. Compositio Math., 126(1):123, 2001. (Cited on pages 244 and 245.)Google Scholar
Grosse-Brauckmann, Isabell. The Fano variety of lines. www.math.uni-bonn.de/people/huybrech/Grosse-BrauckmannBach.pdf. Bachelor thesis, Univ. Bonn. 2014. (Cited on page 104.)Google Scholar
Grothendieck, Alexander. Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux. (Séminaire de Géométrie Algébrique du Bois-Marie 1962), Vol. 2 of Advanced Studies in Pure Math. Amsterdam: North-Holland, 1973. (Cited on pages 1 and 4.)Google Scholar
Grothendieck, Alexander. Sur quelques points d’algèbre homologique. Tôhoku Math. J. (2), 9:119221, 1957. (Cited on page 114.)Google Scholar
Grothendieck, Alexander. Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki]. Paris: Secrétariat mathématique, 1962. (Cited on pages 76 and 82.)Google Scholar
Grothendieck, Alexander. On the de Rham cohomology of algebraic varieties. Inst. Hautes Études Sci. Publ. Math., (29):95–103, 1966. (Cited on page 55.)Google Scholar
Guletskiĭ, Vladimir. Motivic obstruction to rationality of a very general cubic hypersurface in ℙ5. arXiv:1605.09434. (Cited on page 404.)Google Scholar
Gwena, Tawanda. Degenerations of cubic threefolds and matroids. Proc. Amer. Math. Soc., 133(5):13171323, 2005. (Cited on page 239.)Google Scholar
Hahn, Marvin, Lamboglia, Sara, and Vargas, Alejandro. A short note on Cayley–Salmon equations. Matematiche (Catania), 75(2):559574, 2020. (Cited on page 174.)Google Scholar
Hamm, Helmut and Tráng, Lê Dũng. Un théorème de Zariski du type de Lefschetz. Ann. Sci. École Norm. Sup. (4), 6:317355, 1973. (Cited on page 27.)Google Scholar
Han, Frédéric. Pfaffian bundles on cubic surfaces and configurations of planes. Math. Z., 278(1–2):363383, 2014. (Cited on page 173.)Google Scholar
Harris, Joe. Galois groups of enumerative problems. Duke Math. J., 46(4):685724, 1979. (Cited on pages 29, 163, 164, 180, and 181.)Google Scholar
Harris, Joe. Algebraic geometry, Vol. 133 of Graduate Texts in Mathematics. New York: Springer-Verlag, 1995. A first course, Corrected reprint of the 1992 original. (Cited on pages 108 and 277.)Google Scholar
Harris, Joe and Tu, Loring W.. On symmetric and skew-symmetric determinantal varieties. Topology, 23(1):7184, 1984. (Cited on page 323.)Google Scholar
Hartshorne, Robin. Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Math., No. 20. Berlin, New York: Springer-Verlag, 1966. (Cited on page 45.)Google Scholar
Hartshorne, Robin. Algebraic geometry, Vol. 52 of Graduate Texts in Mathematics. New York, Heidelberg: Springer-Verlag, 1977. (Cited on pages 19, 21, 35, 47, 156, 163, 164, 167, 168, 207, 211, 232, and 286.)Google Scholar
Hartshorne, Robin. Deformation theory, Vol. 257 of Graduate Texts in Mathematics. New York: Springer, 2010. (Cited on page 81.)Google Scholar
Hassett, Brendan. Special cubic hypersurfaces of dimension four. ProQuest LLC, Ann Arbor, MI, 1996. PhD thesis, Harvard University. (Cited on pages 281, 289, and 335.)Google Scholar
Hassett, Brendan. Some rational cubic fourfolds. J. Algebraic Geom., 8(1):103114, 1999. (Cited on page 337.)Google Scholar
Hassett, Brendan. Special cubic fourfolds. Compositio Math., 120(1):123, 2000. (Cited on pages 13, 256, 265, 267, 269, 271, 272, 285, 330, 333, 336, 340, 343, 345, and 349.)Google Scholar
Hassett, Brendan. Cubic fourfolds, K3 surfaces, and rationality questions. In Rationality problems in algebraic geometry, Vol. 2172 of Lecture Notes in Math., pp. 2966. Cham: Springer, 2016. (Cited on pages 65, 256, 287, 289, 337, 338, and 402.)Google Scholar
Henderson, Archibald. The twenty-seven lines upon the cubic surface. Reprinting of Cambridge Tracts in Mathematics and Mathematical Physics, No. 13. New York: Hafner Publishing Co., 1960. (Cited on pages 156, 175, 177, and 183.)Google Scholar
Hilbert, David. Ueber die vollen Invariantensysteme. Math. Ann., 42(3):313373, 1893. (Cited on page 185.)Google Scholar
Hilbert, David and Cohn-Vossen, Stefan. Anschauliche Geometrie. Wissenschaftliche Buchgesellschaft, Darmstadt, 1973. Mit einem Anhang: “Einfachste Grundbegriffe der Topologie” von Paul Alexandroff, Reprint der 1932 Ausgabe. (Cited on page 179.)Google Scholar
Hille, Lutz and Van den Bergh, Michel. Fourier–Mukai transforms. In Handbook of tilting theory, Vol. 332 of London Math. Soc. Lecture Note Ser., pp. 147177. Cambridge: Cambridge University Press, 2007. (Cited on page 383.)Google Scholar
Hirschfeld, James. The double-six of lines over PG(3, 4). J. Austral. Math. Soc., 4:8389, 1964. (Cited on page 181.)Google Scholar
Hirschfeld, James. Finite projective spaces of three dimensions. Oxford Mathematical Monographs. New York: Oxford University Press, 1985. Oxford Science Publications. (Cited on page 182.)Google Scholar
Hirzebruch, Friedrich. Topological methods in algebraic geometry. Classics in Mathematics. Berlin: Springer-Verlag, 1995. (Cited on pages 8 and 10.)Google Scholar
Hosoh, Toshio. Automorphism groups of cubic surfaces. J. Algebra, 192(2):651677, 1997. (Cited on page 40.)Google Scholar
Howard, Alan and Sommese, Andrew. On the orders of the automorphism groups of certain projective manifolds. In Manifolds and Lie groups (Notre Dame, Ind., 1980), Vol. 14 of Progr. Math., pp. 145158. Boston, MA: Birkhäuser, 1981. (Cited on page 40.)Google Scholar
Howard, Benjamin, Millson, John, Snowden, Andrew, and Vakil, Ravi. The geometry of eight points in projective space: representation theory, Lie theory and dualities. Proc. Lond. Math. Soc. (3), 105(6):12151244, 2012. (Cited on page 245.)Google Scholar
Hu, Xuntao. The locus of plane quartics with a hyperflex. Proc. Amer. Math. Soc., 145(4):13991413, 2017. (Cited on page 180.)Google Scholar
Hulek, Klaus and Kloosterman, Remke. The L-series of a cubic fourfold. Manuscripta Math., 124(3):391407, 2007. (Cited on page 65.)Google Scholar
Hulek, Klaus and Laface, Roberto. On the Picard numbers of Abelian varieties. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 19(3):11991224, 2019. (Cited on page 216.)Google Scholar
Hulek, Klaus and Sankaran, Gregory. The geometry of Siegel modular varieties. In Higher dimensional birational geometry (Kyoto, 1997), Vol. 35 of Adv. Stud. Pure Math., pp. 89156. Tokyo: Math. Soc. Japan, 2002. (Cited on page 245.)Google Scholar
Hunt, Bruce. The geometry of some special arithmetic quotients, Vol. 1637 of Lecture Notes in Mathe. Berlin: Springer-Verlag, 1996. (Cited on page 174.)Google Scholar
Huybrechts, Daniel. Nodal quintic surfaces and lines on cubic fourfolds. arXiv:2108.10532. (Cited on pages 106, 296, 323, and 325.)Google Scholar
Huybrechts, Daniel. Complex geometry. Berlin: Universitext, Springer-Verlag, 2005. An introduction. (Cited on pages 8 and 10.)Google Scholar
Huybrechts, Daniel. Fourier–Mukai transforms in algebraic geometry. Oxford Mathematical Monographs. Oxford: Oxford University Press, 2006. (Cited on pages 83, 276, 355, 356, 357, 358, 361, 365, 367, 387, 389, 390, 391, and 399.)Google Scholar
Huybrechts, Daniel. The global Torelli theorem: classical, derived, twisted. In Algebraic geometry—Seattle 2005. 1, Vol. 80 of Proc. Sympos. Pure Math., pp. 235258. Providence, RI: Amer. Math. Soc., 2009. (Cited on page 355.)Google Scholar
Huybrechts, Daniel. A global Torelli theorem for hyperkähler manifolds [after M. Verbitsky], Séminaire Bourbaki, Exposé 1040, 2010/2011. Astérisque, 348:375403, 2012. (Cited on pages 295 and 348.)Google Scholar
Huybrechts, Daniel. Lectures on K3 surfaces, Vol. 158 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2016. (Cited on pages 13, 23, 34, 140, 141, 142, 143, 148, 158, 162, 227, 260, 261, 264, 267, 295, 298, 302, 330, 331, 336, 339, 346, 350, 393, 394, and 395.)Google Scholar
Huybrechts, Daniel. The K3 category of a cubic fourfold. Compositio Math., 153(3):586620, 2017. (Cited on pages 339, 341, 385, 393, 394, and 395.)Google Scholar
Huybrechts, Daniel. Motives of derived equivalent K3 surfaces. Abh. Math. Semin. Univ. Hambg., 88(1):201207, 2018. (Cited on page 406.)Google Scholar
Huybrechts, Daniel. Hodge theory of cubic fourfolds, their Fano varieties, and associated K3 categories. In Hochenegger, Andreas, Lehn, Manfred, and Stellari, Paolo (eds.), Birational geometry of hypersurfaces, Vol. 26 of Lect. Notes Unione Mat. Ital., pp. 165198. Cham: Springer, 2019. (Cited on pages 330, 332, 333, 334, 336, 339, 340, 341, 344, 345, and 347.)Google Scholar
Huybrechts, Daniel and Lehn, Manfred. The geometry of moduli spaces of sheaves. Cambridge Mathematical Library. Cambridge: Cambridge University Press, 2nd ed., 2010. (Cited on pages 33, 34, 76, 81, 82, 293, 382, and 397.)Google Scholar
Huybrechts, Daniel and Nieper-Wisskirchen, Marc. Remarks on derived equivalences of Ricci-flat manifolds. Math. Z., 267(3–4):939963, 2011. (Cited on page 293.)Google Scholar
Huybrechts, Daniel and Rennemo, Jørgen. Hochschild cohomology versus the Jacobian ring and the Torelli theorem for cubic fourfolds. Algebr. Geom., 6(1):7699, 2019. (Cited on pages 300, 347, 369, and 373.)Google Scholar
Huybrechts, Daniel and Stellari, Paolo. Equivalences of twisted K3 surfaces. Math. Ann., 332(4):901936, 2005. (Cited on page 394.)Google Scholar
Iliev, Atanas and Manivel, Laurent. Cubic hypersurfaces and integrable systems. Amer. J. Math., 130(6):14451475, 2008. (Cited on pages 299, 317, and 318.)Google Scholar
Iliev, Atanas and Markushevich, Dimitri. The Abel–Jacobi map for a cubic threefold and periods of Fano threefolds of degree 14. Doc. Math., 5:2347, 2000. (Cited on page 220.)Google Scholar
Iskovskikh, Vasiliǐ and Prokhorov, Yuri. Fano varieties. In Algebraic geometry, V, Vol. 47 of Encyclopaedia Math. Sci., pp. 1247. Berlin: Springer, Berlin, 1999. (Cited on page 37.)Google Scholar
Izadi, Elham. A Prym construction for the cohomology of a cubic hypersurface. Proc. London Math. Soc. (3), 79(3):535568, 1999. (Cited on page 128.)Google Scholar
Janssen, Wilhelmus. Skew-symmetric vanishing lattices and their monodromy groups. Math. Ann., 266(1):115133, 1983. (Cited on page 29.)Google Scholar
Javanpeykar, Ariyan and Loughran, Daniel. The moduli of smooth hypersurfaces with level structure. Manuscripta Math., 154(1–2):1322, 2017. (Cited on page 39.)Google Scholar
Kaenders, Rainer. Die Diagonalfläche aus Keramik. Mitteilungen der Deutschen Mathematiker-Vereinigung, 4:1621, 1999. (Cited on page 182.)Google Scholar
Kalck, Martin, Pavic, Nebojsa, and Shinder, Evgeny. Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory. Mosc. Math. J., 21(3):567592, 2021. (Cited on page 377.)Google Scholar
Kalker, Antonius. Cubic fourfolds with fifteen ordinary double points. PhD thesis, Leiden University, 1986. (Cited on page 68.)Google Scholar
Kapranov, Mikhai. On the derived categories of coherent sheaves on some homogeneous spaces. Invent. Math., 92(3):479508, 1988. (Cited on page 364.)Google Scholar
Kapustin, Anton and Li, Yi. D-branes in topological minimal models: the Landau–Ginzburg approach. J. High Energy Phys., (7):045, 26, 2004. (Cited on page 372.)Google Scholar
Kasner, Edward. The double-six configuration connected with the cubic surface, and a related group of Cremona transformations. Amer. J. Math., 25(2):107122, 1903. (Cited on page 179.)Google Scholar
Kass, Jesse and Wickelgren, Kirsten. An arithmetic count of the lines on a smooth cubic surface. Compositio Math., 157(4):677709, 2021. (Cited on pages 156 and 183.)Google Scholar
Katz, Nicholas and Sarnak, Peter. Random matrices, Frobenius eigenvalues, and monodromy, Vol. 45 of American Mathematical Society Colloquium Publications. Providence, RI: Amer. Math. Soc., 1999. (Cited on pages 18, 32, 34, 137, and 138.)Google Scholar
Keneshlou, Hanieh. Cubic surfaces on the singular locus of the Eckardt hypersurface. Matematiche (Catania), 75(2):507516, 2020. (Cited on page 182.)Google Scholar
Kimura, Shun-Ichi. Chow groups are finite dimensional, in some sense. Math. Ann., 331(1):173201, 2005. (Cited on pages 228 and 404.)Google Scholar
Kirwan, Frances. Cohomology of quotients in symplectic and algebraic geometry, Vol. 31 of Mathematical Notes. Princeton, NJ: Princeton University Press, 1984. (Cited on page 143.)Google Scholar
Kirwan, Frances. Partial desingularisations of quotients of nonsingular varieties and their Betti numbers. Ann. of Math. (2), 122(1):4185, 1985. (Cited on page 143.)Google Scholar
Kirwan, Frances. Moduli spaces of degree d hypersurfaces in Pn. Duke Math. J., 58(1):3978, 1989. (Cited on pages 143 and 147.)Google Scholar
Klein, Felix. Ueber Flächen dritter Ordnung. Math. Ann., 6(4):551581, 1873. (Cited on page 174.)Google Scholar
Klein, Felix. The Evanston Colloquium lectures on mathematics, delivered at Northwestern University Aug. 28 to Sept. 1893. Reported by Alexander Ziwet. 2nd ed. New York: Amer. Math. Soc. XI + 109 S. 8 (1894)., 1894. (Cited on page 183.)Google Scholar
Knapp, Anthony. Elliptic curves, Vol. 40 of Mathematical Notes. Princeton, NJ: Princeton University Press, 1992. (Cited on page 21.)Google Scholar
Kodaira, Kunihiko and Spencer, Donald. On deformations of complex analytic structures. I, II. Ann. of Math. (2), 67:328466, 1958. (Cited on page 32.)Google Scholar
Koike, Kenji. Moduli space of Hessian K3 surfaces and arithmetic quotients. arXiv:1002.2854. (Cited on page 185.)Google Scholar
Kollár, János. Rational curves on algebraic varieties, volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. Berlin: Springer-Verlag, 1996. (Cited on pages 81, 84, and 197.)Google Scholar
Kollár, János. Fundamental groups of rationally connected varieties. Michigan Math. J., 48:359368, 2000. Dedicated to William Fulton on the occasion of his 60th birthday. (Cited on page 89.)Google Scholar
Kollár, János. Unirationality of cubic hypersurfaces. J. Inst. Math. Jussieu, 1(3):467476, 2002. (Cited on page 87.)Google Scholar
Kollár, János, Smith, Karen, and Corti, Alessio. Rational and nearly rational varieties, Vol. 92 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2004. (Cited on pages 156 and 158.)Google Scholar
Kontsevich, Maxim and Tschinkel, Yuri. Specialization of birational types. Invent. Math., 217(2):415432, 2019. (Cited on pages 239, 271, 289, and 337.)Google Scholar
Kraft, Hanspeter, Slodowy, Peter, and Springer, Tonny (eds.). Algebraische Transformationsgruppen und Invariantentheorie, Vol. 13 of DMV Seminar. Basel: Birkhäuser Verlag, 1989. (Cited on page 141.)Google Scholar
Krämer, Thomas. Summands of theta divisors on Jacobians. Compositio Math., 156(7):14571475, 2020. (Cited on page 227.)Google Scholar
Krug, Andreas, Ploog, David, and Sosna, Pawel. Derived categories of resolutions of cyclic quotient singularities. Q. J. Math., 69(2):509548, 2018. (Cited on page 398.)Google Scholar
Kudla, Stephen and Rapoport, Michael. On occult period maps. Pacific J. Math., 260(2):565581, 2012. (Cited on pages 186, 246, and 249.)Google Scholar
Kulkarni, Ravindra and Wood, John. Topology of nonsingular complex hypersurfaces. Adv. in Math., 35(3):239263, 1980. (Cited on pages 15 and 24.)Google Scholar
Kunz, Ernst. Residues and duality for projective algebraic varieties, volume 47 of University Lecture Series. Providence, RI: Amer. Math. Soc. 2008. With the assistance of and contributions by David A. Cox and Alicia Dickenstein. (Cited on page 44.)Google Scholar
Kuznetsov, Alexander. Hochschild homology and semiorthogonal decompositions. arXiv:0904.4330. (Cited on pages 361, 369, and 384.)Google Scholar
Kuznetsov, Alexander. Homological projective duality for Grassmannians of lines. arXiv:math/0610957. (Cited on page 389.)Google Scholar
Kuznetsov, Alexander. Derived categories of quadric fibrations and intersections of quadrics. Adv. Math., 218(5):13401369, 2008. (Cited on pages 379 and 388.)Google Scholar
Kuznetsov, Alexander. Lefschetz decompositions and categorical resolutions of singularities. Selecta Math. (N.S.), 13(4):661696, 2008. (Cited on page 392.)Google Scholar
Kuznetsov, Alexander. Derived categories of cubic fourfolds. In Cohomological and geometric approaches to rationality problems, Vol. 282 of Progr. Math., pp. 219243. Boston, MA: Birkhäuser Boston, 2010. (Cited on pages 263, 384, 385, 386, 391, and 392.)Google Scholar
Kuznetsov, Alexander. Base change for semiorthogonal decompositions. Compositio Math., 147(3):852876, 2011. (Cited on pages 367 and 369.)Google Scholar
Kuznetsov, Alexander. Derived categories view on rationality problems. In Rationality problems in algebraic geometry, Vol. 2172 of Lecture Notes in Math., pp. 67104. Cham: Springer, 2016. (Cited on pages 262, 384, and 386.)Google Scholar
Kuznetsov, Alexander. Calabi–Yau and fractional Calabi–Yau categories. J. Reine Angew. Math., 753:239267, 2019. (Cited on page 366.)Google Scholar
Kuznetsov, Alexander and Markushevich, Dimitri. Symplectic structures on moduli spaces of sheaves via the Atiyah class. J. Geom. Phys., 59(7):843860, 2009. (Cited on pages 365 and 397.)Google Scholar
Kuznetsov, Alexander and Perry, Alexander. Homological projective duality for quadrics. J. Algebraic Geom., 30(3):457476, 2021. (Cited on page 364.)Google Scholar
Lahoz, Martí, Lehn, Manfred, Macrì, Emanuele, and Stellari, Paolo. Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects. J. Math. Pures Appl. (9), 114:85117, 2018. (Cited on page 396.)Google Scholar
Lahoz, Martí, Naranjo, Juan Carlos, and Rojas, Andrés. Geometry of Prym semicanonical pencils and an application to cubic threefolds. arXiv:2106.08683. (Cited on page 199.)Google Scholar
Lai, Kuan-Wen. New cubic fourfolds with odd-degree unirational parametrizations. Algebr Number Theory, 11(7):15971626, 2017. (Cited on pages 148, 338, 349, and 402.)Google Scholar
Lange, Herbert and Birkenhake, Christina. Complex abelian varieties, Vol. 302 of Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag, 1992. (Cited on pages 216, 221, 222, and 226.)Google Scholar
Larsen, Michael and Lunts, Valery. Motivic measures and stable birational geometry. Mosc. Math. J., 3(1):8595, 259, 2003. (Cited on pages 111 and 240.)Google Scholar
Laterveer, Robert. A remark on the motive of the Fano variety of lines of a cubic. Ann. Math. Qué., 41(1):141154, 2017. (Cited on pages 113, 306, 404, and 405.)Google Scholar
Laterveer, Robert. A family of cubic fourfolds with finite-dimensional motive. J. Math. Soc. Japan, 70(4):14531473, 2018. (Cited on pages 306 and 405.)Google Scholar
Laterveer, Robert. Lagrangian subvarieties in the Chow ring of some hyperkähler varieties. Mosc. Math. J., 18(4):693719, 2018. (Cited on page 321.)Google Scholar
Lauter, Kristin. Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields. J. Algebraic Geom., 10(1):1936, 2001. With an appendix in French by J.-P. Serre. (Cited on page 236.)Google Scholar
Laza, Radu. The moduli space of cubic fourfolds. J. Algebraic Geom., 18(3):511545, 2009. (Cited on pages 350 and 352.)Google Scholar
Laza, Radu. The moduli space of cubic fourfolds via the period map. Ann. of Math. (2), 172(1):673711, 2010. (Cited on pages 307 and 349.)Google Scholar
Laza, Radu. Maximally algebraic potentially irrational cubic fourfolds. Proc. Amer. Math. Soc., 149(8):32093220, 2021. (Cited on page 310.)Google Scholar
Laza, Radu, Saccà, Giulia, and Voisin, Claire. A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold. Acta Math., 218(1):55135, 2017. (Cited on page 298.)Google Scholar
Laza, Radu and Zheng, Zhiwei. Automorphisms and periods of cubic fourfolds. Math. Z., 300(2):14551507, 2022. (Cited on page 40.)Google Scholar
Lazarsfeld, Robert. Positivity in algebraic geometry. II, Vol. 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. (Cited on page 103.)Google Scholar
Le Potier, Joseph. Lectures on vector bundles, Vol. 54 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 1997. Translated by A. Maciocia. (Cited on pages 135 and 136.)Google Scholar
Lehn, Christian. Twisted cubics on singular cubic fourfolds–on Starr’s fibration. Math. Z., 290(1–2):379388, 2018. (Cited on page 269.)Google Scholar
Lehn, Christian, Lehn, Manfred, Sorger, Christoph, and van Straten, Duco. Twisted cubics on cubic fourfolds. J. Reine Angew. Math., 731:87128, 2017. (Cited on page 342.)Google Scholar
Li, Chunyi, Pertusi, Laura, and Zhao, Xiaolei. Derived categories of hearts on Kuznetsov components. arXiv:2203.13864. (Cited on page 394.)Google Scholar
Libgober, Anatoly. On the fundamental group of the space of cubic surfaces. Math. Z., 162(1):6367, 1978. (Cited on page 147.)Google Scholar
Libgober, Anatoly and Wood, John. On the topological structure of even-dimensional complete intersections. Trans. Amer. Math. Soc., 267(2):637660, 1981. (Cited on page 14.)Google Scholar
Liu, Yuchen. K-stability of cubic fourfolds. J. Reine Angew. Math., 786:5577, 2022. (Cited on page 353.)Google Scholar
Liu, Yuchen and Xu, Chenyang. K-stability of cubic threefolds. Duke Math. J., 168(11):20292073, 2019. (Cited on page 244.)Google Scholar
Lönne, Michael. Fundamental groups of projective discriminant complements. Duke Math. J., 150(2):357405, 2009. (Cited on page 147.)Google Scholar
Looijenga, Eduard. Isolated singular points on complete intersections, Vol. 77 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 1984. (Cited on page 29.)Google Scholar
Looijenga, Eduard. The period map for cubic fourfolds. Invent. Math., 177(1):213233, 2009. (Cited on pages 300, 308, 347, and 349.)Google Scholar
Looijenga, Eduard. Teichmüller spaces and Torelli theorems for hyperkähler manifolds. Math. Z., 298(1–2):261279, 2021. (Cited on pages 295 and 348.)Google Scholar
Looijenga, Eduard and Swierstra, Rogier. The period map for cubic threefolds. Compositio Math., 143(4):10371049, 2007. (Cited on pages 246 and 248.)Google Scholar
Ma, Shouhei. On the Kodaira dimension of orthogonal modular varieties. Invent. Math., 212(3):859911, 2018. (Cited on page 349.)Google Scholar
Macdonald, Ian. The Poincaré polynomial of a symmetric product. Proc. Cambridge Philos. Soc., 58:563568, 1962. (Cited on page 114.)Google Scholar
Macrì, Emanuele and Stellari, Paolo. Fano varieties of cubic fourfolds containing a plane. Math. Ann., 354(3):11471176, 2012. (Cited on page 341.)Google Scholar
Macrì, Emanuele and Stellari, Paolo. Lectures on non-commutative K3 surfaces, Bridgeland stability, and moduli spaces. In Hochenegger, Andreas, Lehn, Manfred, and Stellari, Paolo (eds.), Birational geometry of hypersurfaces, Vol. 26 of Lect. Notes Unione Mat. Ital., pp. 199265. Cham: Springer, 2019. (Cited on page 309.)Google Scholar
Manin, Yuri. Correspondences, motifs and monoidal transformations. Mat. Sb. (N.S.), 77 (119):475507, 1968. (Cited on page 229.)Google Scholar
Manin, Yuri. Cubic forms, Vol. 4 of North-Holland Mathematical Library. Amsterdam: North-Holland Publishing Co., 2nd ed. 1986. Algebra, geometry, arithmetic, Translated from the Russian by M. Hazewinkel. (Cited on pages 156, 158, 159, and 170.)Google Scholar
Manivel, Laurent and Mezzetti, Emilia. On linear spaces of skew-symmetric matrices of constant rank. Manuscripta Math., 117(3):319331, 2005. (Cited on page 276.)Google Scholar
Markman, Eyal. A survey of Torelli and monodromy results for holomorphic-symplectic varieties. In Complex and differential geometry, Vol. 8 of Springer Proc. Math., pp. 257322. Heidelberg: Springer, 2011. (Cited on pages 295, 308, 309, 341, and 348.)Google Scholar
Markman, Eyal. Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections. Kyoto J. Math., 53(2):345403, 2013. (Cited on pages 308 and 326.)Google Scholar
Markman, Eyal. Lagrangian fibrations of holomorphic-symplectic varieties of K3[n]-type. In Algebraic and complex geometry, Vol. 71 of Springer Proc. Math. Stat., pp. 241283. Cham: Springer, 2014. (Cited on page 342.)Google Scholar
Markushevich, Dimitri and Roulleau, Xavier. Irrationality of generic cubic threefold via Weil’s conjectures. Commun. Contemp. Math., 20(7):1750078, 12, 2018. (Cited on page 238.)Google Scholar
Markushevich, Dimitri and Tikhomirov, Alexander. The Abel–Jacobi map of a moduli component of vector bundles on the cubic threefold. J. Algebraic Geom., 10(1):3762, 2001. (Cited on page 220.)Google Scholar
Mather, John and Yau, Stephen S. T.. Classification of isolated hypersurface singularities by their moduli algebras. Invent. Math., 69(2):243251, 1982. (Cited on page 46.)Google Scholar
Matsumura, Hideyuki. Commutative algebra, Vol. 56 of Mathematics Lecture Note Series. Reading, MA: Benjamin/Cummings Publishing Co., Inc., 2nd ed. 1980. (Cited on page 31.)Google Scholar
Matsumura, Hideyuki and Monsky, Paul. On the automorphisms of hypersurfaces. J. Math. Kyoto Univ., 3:347361, 1963/1964. (Cited on pages 34 and 38.)Google Scholar
Matsusaka, Teruhisa. On a characterization of a Jacobian variety. Mem. Coll. Sci. Univ. Kyoto Ser. A. Math., 32:119, 1959. (Cited on page 227.)Google Scholar
Matsusaka, Teruhisa and Mumford, David. Two fundamental theorems on deformations of polarized varieties. Amer. J. Math., 86:668684, 1964. (Cited on page 35.)Google Scholar
Maxim, Laurentiu and Schürmann, Jörg. Twisted genera of symmetric products. Selecta Math. (N.S.), 18(1):283317, 2012. (Cited on page 121.)Google Scholar
Mayanskiy, Evgeny. Intersection lattices of cubic fourfolds. arXiv:1112.0806. (Cited on page 332.)Google Scholar
Mboro, René. Remarks on the CH2 of cubic hypersurfaces. Geom. Dedicata, 200:125, 2019. (Cited on page 401.)Google Scholar
McKean, Stephen. Rational lines on smooth cubic surfaces. arXiv:2101.08217. (Cited on page 183.)Google Scholar
Meachan, Ciaran. A note on spherical functors. Bull. Lond. Math. Soc., 53(3):956962, 2021. (Cited on page 398.)Google Scholar
Milne, James. Jacobian varieties. In Arithmetic geometry (Storrs, Conn., 1984), pp. 167212. New York: Springer, 1986. (Cited on page 236.)Google Scholar
Miranda, Rick. Triple covers in algebraic geometry. Amer. J. Math., 107(5):11231158, 1985. (Cited on page 66.)Google Scholar
Mongardi, Giovanni and Ottem, John Christian. Curve classes on irreducible holomorphic symplectic varieties. Commun. Contemp. Math., 22(7):1950078, 15, 2020. (Cited on pages 309, 310, and 330.)Google Scholar
Moschetti, Riccardo. The derived category of a non generic cubic fourfold containing a plane. Math. Res. Lett., 25(5):15251545, 2018. (Cited on page 385.)Google Scholar
Mukai, Shigeru. An introduction to invariants and moduli, Vol. 81 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2003. Translated from the 1998 and 2000 Japanese editions by W. M. Oxbury. (Cited on pages 135, 139, 147, 185, and 186.)Google Scholar
Mukai, Shigeru and Nasu, Hirokazu. Obstructions to deforming curves on a 3-fold. I. A generalization of Mumford’s example and an application to Hom schemes. J. Algebraic Geom., 18(4):691709, 2009. (Cited on page 70.)Google Scholar
Mumford, David. Theta characteristics of an algebraic curve. Ann. Sci. École Norm. Sup. (4), 4:181192, 1971. (Cited on page 180.)Google Scholar
Mumford, David. Prym varieties. I. In Contributions to analysis (a collection of papers dedicated to Lipman Bers), pp. 325350. New York: Academic Press, 1974. (Cited on pages 221 and 238.)Google Scholar
Mumford, David. Hilbert’s fourteenth problem–the finite generation of subrings such as rings of invariants. In Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Vol. XXVIII, Northern Illinois Univ., De Kalb, Ill., 1974), pp. 431444. Providence, RI: Amer. Math. Soc., 1976. (Cited on page 135.)Google Scholar
Mumford, David. Stability of projective varieties. Enseign. Math. (2), 23(1–2):39110, 1977. (Cited on pages 147 and 185.)Google Scholar
Mumford, David, Fogarty, John, and Kirwan, Frances. Geometric invariant theory, Vol. 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete (2). Berlin: Springer-Verlag, 3rd ed., 1994. (Cited on pages 135, 136, 137, and 139.)Google Scholar
Murfet, Daniel. Residues and duality for singularity categories of isolated Gorenstein singularities. Compositio Math., 149(12):20712100, 2013. (Cited on pages 372 and 374.)Google Scholar
Murre, Jacob. Algebraic equivalence modulo rational equivalence on a cubic threefold. Compositio Math., 25:161206, 1972. (Cited on pages 193, 197, 198, 228, and 229.)Google Scholar
Murre, Jacob. Reduction of the proof of the non-rationality of a non-singular cubic threefold to a result of Mumford. Compositio Math., 27:6382, 1973. (Cited on pages 193, 221, and 238.)Google Scholar
Murre, Jacob. Some results on cubic threefolds. In Classification of algebraic varieties and compact complex manifolds, Vol. 412 of Lecture Notes in Math., pp. 140160. Berlin: Springer, 1974. (Cited on page 228.)Google Scholar
Murre, Jacob, Nagel, Jan, and Peters, Chris. Lectures on the theory of pure motives, Vol. 61 of University Lecture Series. Providence, RI: Amer. Math. Soc. 2013. (Cited on pages 4 and 112.)Google Scholar
Nagel, Jan and Saito, Morihiko. Relative Chow–Künneth decompositions for conic bundles and Prym varieties. Int. Math. Res. Not. IMRN, (16):2978–3001, 2009. (Cited on page 229.)Google Scholar
Nakamura, Iku. Planar cubic curves, from Hesse to Mumford. Vol. 17, pp. 73101. 2004. Sugaku Expositions. (Cited on page 147.)Google Scholar
Naruki, Isao. Cross ratio variety as a moduli space of cubic surfaces. Proc. London Math. Soc. (3), 45(1):130, 1982. With an appendix by Eduard Looijenga. (Cited on page 185.)Google Scholar
Nicaise, Johannes and Shinder, Evgeny. The motivic nearby fiber and degeneration of stable rationality. Invent. Math., 217(2):377413, 2019. (Cited on pages 239, 271, 289, and 337.)Google Scholar
Nuer, Howard. Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces. Algebr. Geom., 4(3):281289, 2017. (Cited on page 348.)Google Scholar
Oberdieck, Georg, Shen, Junliang, and Yin, Qizheng. Rational curves in holomorphic symplectic varieties and Gromov–Witten invariants. Adv. Math., 357:106829, 8, 2019. (Cited on pages 318, 319, and 329.)Google Scholar
O’Grady, Kieran G.. Desingularized moduli spaces of sheaves on a K3. J. Reine Angew. Math., 512:49117, 1999. (Cited on page 298.)Google Scholar
Orlik, Peter and Solomon, Louis. Singularities. II. Automorphisms of forms. Math. Ann., 231(3):229240, 1977/78. (Cited on pages 34 and 46.)Google Scholar
Orlov, Dimitri. Triangulated categories of singularities and D-branes in Landau–Ginzburg models. Tr. Mat. Inst. Steklova, 246:240262, 2004. (Cited on page 372.)Google Scholar
Orlov, Dmitri. Derived categories of coherent sheaves and equivalences between them. Uspekhi Mat. Nauk, 58(3(351)):89172, 2003. (Cited on page 355.)Google Scholar
Orlov, Dmitri. Derived categories of coherent sheaves and triangulated categories of singularities. In Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II, Vol. 270 of Progr. Math., pp. 503531. Boston, MA: Birkhäuser Boston, 2009. (Cited on pages 372 and 373.)Google Scholar
Oscari, David. Cubic surfaces as Pfaffians. arXiv:1911.09754. (Cited on page 173.)Google Scholar
Ottaviani, Giorgio. Spinor bundles on quadrics. Trans. Amer. Math. Soc., 307(1):301316, 1988. (Cited on page 364.)Google Scholar
Ottem, John Christian. Nef cycles on some hyperkähler fourfolds. In Facets of algebraic geometry. Vol. II, Vol. 473 of London Math. Soc. Lecture Note Ser., pp. 228237. Cambridge: Cambridge University Press, 2022. (Cited on page 317.)Google Scholar
Ouchi, Genki. Lagrangian embeddings of cubic fourfolds containing a plane. Compositio Math., 153(5):947972, 2017. (Cited on page 397.)Google Scholar
Pan, Xuanyu. Automorphism and cohomology I: Fano varieties of lines and cubics. Algebr. Geom., 7(1):129, 2020. (Cited on pages 39 and 215.)Google Scholar
Paranjape, Kapil H.. Cohomological and cycle-theoretic connectivity. Ann. of Math. (2), 139(3):641660, 1994. (Cited on pages 5 and 400.)Google Scholar
Perry, Alexander. The integral Hodge conjecture for two-dimensional Calabi–Yau categories. Compositio Math., 158(2):287333, 2022. (Cited on page 383.)Google Scholar
Pertusi, Laura. Fourier–Mukai partners for very general special cubic fourfolds. Math. Res. Lett., 28(1):213243, 2021. (Cited on page 395.)Google Scholar
Peters, Chris. On a motivic interpretation of primitive, variable and fixed cohomology. Math. Nachr., 292(2):402408, 2019. (Cited on pages 5 and 403.)Google Scholar
Peters, Chris and Steenbrink, Joseph. Degeneration of the Leray spectral sequence for certain geometric quotients, Moscow Math. Journal, 2(3): 10851095, 2003. Dedicated to Vladimir Igorevich Arnold on the occasion of his 65th birthday. (Cited on pages 144, 145, and 146.)Google Scholar
Peters, Chris and Steenbrink, Joseph. Monodromy of variations of Hodge structure, Acta Appl. Math., 75:183194, 2003. Monodromy and differential equations (Moscow, 2001). (Cited on page 25.)Google Scholar
Peters, Chris and Steenbrink, Joseph. Mixed Hodge structures, Vol. 52 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. Berlin: Springer-Verlag, 2008. (Cited on page 117.)Google Scholar
Polishchuk, Alexander and Vaintrob, Arkady. Chern characters and Hirzebruch–Riemann–Roch formula for matrix factorizations. Duke Math. J., 161(10):18631926, 2012. (Cited on pages 372 and 374.)Google Scholar
Polo-Blanco, Irene and Top, Jaap. A remark on parameterizing nonsingular cubic surfaces. Comput. Aided Geom. Design, 26(8):842849, 2009. (Cited on page 166.)Google Scholar
Poonen, Bjorn. Varieties without extra automorphisms. III. Hypersurfaces. Finite Fields Appl., 11(2):230268, 2005. (Cited on pages 38 and 40.)Google Scholar
Popov, Pavel. Twisted cubics and quadruples of points on cubic surfaces. arXiv:1810.04563. (Cited on pages 177, 375, and 399.)Google Scholar
Ran, Ziv. On subvarieties of abelian varieties. Invent. Math., 62(3):459479, 1981. (Cited on page 227.)Google Scholar
Ranestad, Kristian and Voisin, Claire. Variety of power sums and divisors in the moduli space of cubic fourfolds. Doc. Math., 22:455504, 2017. (Cited on page 349.)Google Scholar
Rapoport, Michael. Complément à l’article de P. Deligne “La conjecture de Weil pour les surfaces K3”. Invent. Math., 15:227236, 1972. (Cited on page 11.)Google Scholar
Reid, Miles. The complete intersection of two or more quadrics. PhD thesis, University of Cambridge, 1972. (Cited on page 229.)Google Scholar
Reinecke, Emanuel. Moduli space of cubic surfaces. www.math.uni-bonn.de/people/huybrech/Reineckefinal.pdf. Bachelor thesis, University of Bonn, 2012. (Cited on pages 183 and 185.)Google Scholar
Rempel, Max. Positivité des cycles dans les variétés algébriques. PhD thesis, University of Paris, 2012. (Cited on page 317.)Google Scholar
Rieß, Ulrike. On the non-divisorial base locus of big and nef line bundles on K3[2]-type varieties. Proc. Roy. Soc. Edinburgh Sect. A, 151(1):5278, 2021. (Cited on pages 308 and 309.)Google Scholar
Roulleau, Xavier. Elliptic curve configurations on Fano surfaces. Manuscripta Math., 129(3):381399, 2009. (Cited on pages 198 and 215.)Google Scholar
Roulleau, Xavier. The Fano surface of the Klein cubic threefold. J. Math. Kyoto Univ., 49(1):113129, 2009. (Cited on pages 216 and 244.)Google Scholar
Roulleau, Xavier. The Fano surface of the Fermat cubic threefold, the del Pezzo surface of degree 5 and a ball quotient. Proc. Amer. Math. Soc., 139(10):34053412, 2011. (Cited on page 198.)Google Scholar
Roulleau, Xavier. Fano surfaces with 12 or 30 elliptic curves. Michigan Math. J., 60(2):313329, 2011. (Cited on page 216.)Google Scholar
Roulleau, Xavier. Quotients of Fano surfaces. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 23(3):325349, 2012. (Cited on page 215.)Google Scholar
Roulleau, Xavier. On the Tate conjecture for the Fano surfaces of cubic threefolds. J. Number Theory, 133(7):23202323, 2013. (Cited on page 217.)Google Scholar
Russo, Francesco and Staglianò, Giovanni. Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds. Duke Math. J., 168(5):849865, 2019. (Cited on page 337.)Google Scholar
Russo, Francesco and Staglianò, Giovanni. Trisecant flops, their associated K3 surfaces and the rationality of some cubic fourfolds. JEMS (2022), to appear. arXiv:1909.01263. (Cited on page 337.)Google Scholar
Rybakov, Sergey and Trepalin, Andrey. Minimal cubic surfaces over finite fields. Mat. Sb., 208(9):148170, 2017. (Cited on page 159.)Google Scholar
Saccà, Giulia. Birational geometry of the intermediate Jacobian fibration of a cubic fourfold, with an appendix by C. Voisin. arXiv:2002.01420. (Cited on pages 270 and 298.)Google Scholar
Šafarevič, Igor. Basic algebraic geometry. 1. Heidelberg: Springer, 3rd ed. 2013. Varieties in projective space. (Cited on page 159.)Google Scholar
Saito, Kyoji. Einfach-elliptische Singularitäten. Invent. Math., 23:289325, 1974. (Cited on page 45.)Google Scholar
Salmon, George. On the triple tangent planes of surfaces of the third order. Cambridge and Dublin Math. Journal, IV:252260, 1849. (Cited on page 175.)Google Scholar
Salmon, George. On quaternary cubics. Phil. Trans. R. Soc., 150:229239, 1860. (Cited on pages 21 and 184.)Google Scholar
Salmon, George. A treatise on the analytic geometry of three dimensions. Dublin: Hodges, Figgis, 1865. (Cited on page 183.)Google Scholar
Schläfli, Ludwig. An attempt to determine the twenty-seven lines upon a surfaces of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface. Quart. J. Math., 2:110120, 1858. (Cited on page 183.)Google Scholar
Schoen, Chad. Varieties dominated by product varieties. Internat. J. Math., 7(4):541571, 1996. (Cited on page 238.)Google Scholar
Schreieder, Stefan. Theta divisors with curve summands and the Schottky problem. Math. Ann., 365(3–4):10171039, 2016. (Cited on page 237.)Google Scholar
Segre, Beniamino. Le rette delle superficie cubiche nei corpi commutativi. Boll. Un. Mat. Ital. (3), 4:223228, 1949. (Cited on page 183.)Google Scholar
Sernesi, Edoardo. Deformations of algebraic schemes, Vol. 334 of Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag, 2006. (Cited on pages 36, 37, and 81.)Google Scholar
Serre, Jean-Pierre. A course in arithmetic. Vol. 7 of Graduate Texts in Mathematics. New York, Heidelberg: Springer-Verlag. (Cited on pages 12 and 14.)Google Scholar
Serre, Jean-Pierre. On the fundamental group of a unirational variety. J. London Math. Soc., 34:481484, 1959. (Cited on page 88.)Google Scholar
Serre, Jean-Pierre. Local algebra. Springer Monographs in Mathematics. Berlin: Springer-Verlag, 2000. Translated from the French by CheeWhye Chin and revised by the author. (Cited on page 43.)Google Scholar
Shen, Junliang and Yin, Qizheng. K3 categories, one-cycles on cubic fourfolds, and the Beauville–Voisin filtration. J. Inst. Math. Jussieu, 19(5):16011627, 2020. (Cited on page 401.)Google Scholar
Shen, Mingmin. Surfaces with involution and Prym constructions. arXiv:1209.5457. (Cited on pages 105 and 106.)Google Scholar
Shen, Mingmin. On relations among 1-cycles on cubic hypersurfaces. J. Algebraic Geom., 23(3):539569, 2014. (Cited on pages 5, 229, and 400.)Google Scholar
Shen, Mingmin. Hyperkähler manifolds of Jacobian type. J. Reine Angew. Math., 712:189223, 2016. (Cited on pages 264, 294, 295, 311, and 313.)Google Scholar
Shen, Mingmin and Vial, Charles. The Fourier transform for certain hyperkähler fourfolds. Mem. Amer. Math. Soc., 240(1139):vii+163, 2016. (Cited on pages 306, 329, and 401.)Google Scholar
Shiffman, Bernard and Sommese, Andrew. Vanishing theorems on complex manifolds, Vol. 56 of Progress in Mathematics. Boston, MA: Birkhäuser Boston, Inc., 1985. (Cited on page 319.)Google Scholar
Shimada, Ichiro. On the cylinder isomorphism associated to the family of lines on a hyper-surface. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 37(3):703719, 1990. (Cited on pages 127 and 132.)Google Scholar
Shinder, Evgeny. Torsion in the cohomology of Fano varieties of lines. mathoverflow question 434409. (Cited on page 119.)Google Scholar
Shioda, Tetsuji. An example of unirational surfaces in characteristic p. Math. Ann., 211:233236, 1974. (Cited on page 89.)Google Scholar
Shioda, Tetsuji. On unirationality of supersingular surfaces. Math. Ann., 225(2):155159, 1977. (Cited on page 89.)Google Scholar
Shioda, Tetsuji. Some remarks on Abelian varieties. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 24(1):1121, 1977. (Cited on page 117.)Google Scholar
Shioda, Tetsuji. The Hodge conjecture for Fermat varieties. Math. Ann., 245(2):175184, 1979. (Cited on page 72.)Google Scholar
Shioda, Tetsuji and Katsura, Toshiyuki. On Fermat varieties. Tohoku Math. J. (2), 31(1):97115, 1979. (Cited on page 72.)Google Scholar
Si, Fei. Cohomology of moduli space of cubic fourfolds I. arXiv:2103.04282. (Cited on page 353.)Google Scholar
Smith, Roy and Varley, Robert. A Riemann singularities theorem for Prym theta divisors, with applications. Pacific J. Math., 201(2):479509, 2001. (Cited on pages 235 and 238.)Google Scholar
Sommese, Andrew. Complex subspaces of homogeneous complex manifolds. II. Homotopy results. Nagoya Math. J., 86:101129, 1982. (Cited on page 122.)Google Scholar
Stark, Samuel. Deformations of the Fano scheme of a cubic hypersurface. arXiv:2207.08762. (Cited on page 109.)Google Scholar
Swinnerton-Dyer, Peter. Cubic surfaces over finite fields. Math. Proc. Cambridge Philos. Soc., 149(3):385388, 2010. (Cited on page 159.)Google Scholar
Tanimoto, Sho and Várilly-Alvarado, Anthony. Kodaira dimension of moduli of special cubic fourfolds. J. Reine Angew. Math., 752:265300, 2019. (Cited on page 349.)Google Scholar
Tanturri, Fabio. Pfaffian representations of cubic surfaces. Geom. Dedicata, 168:6986, 2014. (Cited on page 173.)Google Scholar
Tevelev, Jenia. Projective duality and homogeneous spaces, Vol. 133 of Encyclopaedia of Mathematical Sciences. Berlin: Springer-Verlag, 2005. Invariant Theory and Algebraic Transformation Groups, IV. (Cited on page 80.)Google Scholar
Tjurin, Andreǐ. The Fano surface of a nonsingular cubic in P4. Izv. Akad. Nauk SSSR Ser. Mat., 34:12001208, 1970. (Cited on pages 193, 210, 215, 225, 230, and 234.)Google Scholar
Tjurin, Andreǐ. The geometry of the Fano surface of a nonsingular cubic F ⊂ ℙ4, and Torelli’s theorems for Fano surfaces and cubics. Izv. Akad. Nauk SSSR Ser. Mat., 35:498529, 1971. (Cited on pages 207 and 236.)Google Scholar
Tjurin, Andreǐ. Five lectures on three-dimensional varieties. Uspehi Mat. Nauk, 27(5):(167), 350, 1972. (Cited on page 193.)Google Scholar
Tjurin, Andreǐ. The intermediate Jacobian of three-dimensional varieties. In Current problems in mathematics, Vol. 12 (Russian), pp. 557, 239 (loose errata). Moscow: VINITI, 1979. (Cited on page 234.)Google Scholar
Togliatti, Eugenio. Una notevole superficie de 5o ordine con soli punti doppi isolati. Vierteljschr. Naturforsch. Ges. Zürich, 85(Beibl, Beiblatt (Festschrift Rudolf Fueter)):127132, 1940. (Cited on page 323.)Google Scholar
Tommasi, Orsola. Stable cohomology of spaces of non-singular hypersurfaces. Adv. Math., 265:428440, 2014. (Cited on page 146.)Google Scholar
Totaro, Burt. The integral cohomology of the Hilbert scheme of two points. Forum Math. Sigma, 4:e8, 20, 2016. (Cited on pages 119 and 294.)Google Scholar
Tregub, Semion. Three constructions of rationality of a cubic fourfold. Vestnik Moskov. Univ. Ser. I Mat. Mekh., (3):8–14, 1984. (Cited on page 289.)Google Scholar
Tregub, Semion. Two remarks on four-dimensional cubics. Uspekhi Mat. Nauk, 48(2(290)):201202, 1993. (Cited on pages 276, 287, and 337.)Google Scholar
Tu, Nguyen Chanh. Non-singular cubic surfaces with star points. Vietnam J. Math., 29(3):287292, 2001. (Cited on page 182.)Google Scholar
Tu, Nguyen Chanh. On semi-stable, singular cubic surfaces. In Singularités Franco-Japonaises, Vol. 10 of Sémin. Congr., pp. 373389. Paris: Soc. Math. France, 2005. (Cited on page 186.)Google Scholar
Vakil, Ravi and Wood, Melanie Matchett. Discriminants in the Grothendieck ring. Duke Math. J., 164(6):11391185, 2015. (Cited on page 146.)Google Scholar
van den Dries, Bart. Degenerations of cubic fourfolds and holomorphic symplectic geometry. PhD thesis, Utrecht University, 2012. (Cited on page 350.)Google Scholar
van der Geer, Gerard. On the geometry of a Siegel modular threefold. Math. Ann., 260(3):317350, 1982. (Cited on page 245.)Google Scholar
van der Geer, Gerard and Kouvidakis, Alexis. A note on Fano surfaces of nodal cubic three-folds. In Algebraic and arithmetic structures of moduli spaces (Sapporo 2007), Vol. 58 of Adv. Stud. Pure Math., pp. 2745. Tokyo: Math. Soc. Japan, 2010. (Cited on pages 239 and 241.)Google Scholar
van der Geer, Gerard and Kouvidakis, Alexis. The rank-one limit of the Fourier–Mukai transform. Doc. Math., 15:747763, 2010. (Cited on page 228.)Google Scholar
van der Waerden, Bartel. A history of algebra. Berlin: Springer-Verlag, 1985. From al-Khwārizmī to Emmy Noether. (Cited on pages 156 and 181.)Google Scholar
van Geemen, Bert. Half twists of Hodge structures of CM-type. J. Math. Soc. Japan, 53(4):813833, 2001. (Cited on page 249.)Google Scholar
van Geemen, Bert and Izadi, Elham. Half twists and the cohomology of hypersurfaces. Math. Z., 242(2):279301, 2002. (Cited on page 72.)Google Scholar
van Opstall, Michael and Veliche, Răzvan. Variation of hyperplane sections. In Algebra, geometry and their interactions, Vol. 448 of Contemp. Math., pp. 255260. Providence, RI: Amer. Math. Soc., 2007. (Cited on page 69.)Google Scholar
Vasil’ev, Victor. How to calculate the homology of spaces of nonsingular algebraic projective hypersurfaces. Tr. Mat. Inst. Steklova, 225(Solitony Geom. Topol. na Perekrest.):132152, 1999. (Cited on page 146.)Google Scholar
Verbitsky, Misha. Mapping class group and a global Torelli theorem for hyperkähler manifolds. Duke Math. J., 162(15):29292986, 2013. Appendix A by E. Markman. (Cited on pages 295 and 348.)Google Scholar
Verbitsky, Misha. Errata for “Mapping class group and a global Torelli theorem for hyper-kähler manifolds” by Misha Verbitsky. Duke Math. J., 169(5):10371038, 2020. (Cited on pages 295 and 348.)Google Scholar
Vial, Charles. Projectors on the intermediate algebraic Jacobians. New York J. Math., 19:793822, 2013. (Cited on page 404.)Google Scholar
Viehweg, Eckart and Zuo, Kang. Complex multiplication, Griffiths–Yukawa couplings, and rigidity for families of hypersurfaces. J. Algebraic Geom., 14(3):481528, 2005. (Cited on page 49.)Google Scholar
Voisin, Claire. Birational invariants and decomposition of the diagonal. In Hochenegger, Andreas, Lehn, Manfred, and Stellari, Paolo (eds.), Birational geometry of hypersurfaces, Vol. 26 of Lect. Notes Unione Mat. Ital., pp. 371. Cham: Springer, 2019. (Cited on page 239.)Google Scholar
Voisin, Claire. Théorème de Torelli pour les cubiques de P5. Invent. Math., 86(3):577601, 1986. (Cited on pages 59, 255, 256, 257, 259, 263, 292, 300, 312, 323, 324, 325, 326, and 347.)Google Scholar
Voisin, Claire. Sur la stabilité des sous-variétés lagrangiennes des variétés symplectiques holomorphes. In Complex projective geometry (Trieste, 1989/Bergen, 1989), Vol. 179 of London Math. Soc. Lecture Note Ser., pp. 294303. Cambridge: Cambridge University Press, 1992. (Cited on page 316.)Google Scholar
Voisin, Claire. Théorie de Hodge et géométrie algébrique complexe, Vol. 10 of Cours Spécialisés. Paris: Société Mathématique de France, 2002. (Cited on pages 1, 24, 27, 28, 29, 45, 47, 49, 50, 52, 57, 116, 118, 133, 153, 266, 324, and 399.)Google Scholar
Voisin, Claire. Intrinsic pseudo-volume forms and K-correspondences. In The Fano Conference, pp. 761792. Turin: Univ. Torino, 2004. (Cited on page 327.)Google Scholar
Voisin, Claire. Some aspects of the Hodge conjecture. Jpn. J. Math., 2(2):261296, 2007. (Cited on pages 309 and 400.)Google Scholar
Voisin, Claire. Erratum: “A Torelli theorem for cubics in ℙ5. Invent. Math., 172(2):455458, 2008. (Cited on pages 255, 300, and 347.)Google Scholar
Voisin, Claire. On the Chow ring of certain algebraic hyper-Kähler manifolds. Pure Appl. Math. Q., 4(3, Special issue: In honor of Fedor Bogomolov. Part 2):613649, 2008. (Cited on pages 401 and 404.)Google Scholar
Voisin, Claire. Coniveau 2 complete intersections and effective cones. Geom. Funct. Anal., 19(5):14941513, 2010. (Cited on pages 214 and 317.)Google Scholar
Voisin, Claire. Abel–Jacobi map, integral Hodge classes and decomposition of the diagonal. J. Algebraic Geom., 22(1):141174, 2013. (Cited on pages 309, 400, and 402.)Google Scholar
Voisin, Claire. Unirational threefolds with no universal codimension 2 cycle. Invent. Math., 201(1):207237, 2015. (Cited on pages 220 and 402.)Google Scholar
Voisin, Claire. Stable birational invariants and the Lüroth problem. In Surveys in differential geometry 2016. Advances in geometry and mathematical physics, Vol. 21 of Surv. Differ. Geom., pp. 313342. Somerville, MA: Int. Press, 2016. (Cited on page 239.)Google Scholar
Voisin, Claire. On the universal CH0 group of cubic hypersurfaces. J. Eur. Math. Soc., 19(6):16191653, 2017. (Cited on pages 26, 112, 239, 402, and 403.)Google Scholar
Voisin, Claire. Hyper-Kähler compactification of the intermediate Jacobian fibration of a cubic fourfold: the twisted case. In Local and global methods in algebraic geometry, Vol. 712 of Contemp. Math., pp. 341355. Providence, RI: Amer. Math. Soc. 2018. (Cited on page 298.)Google Scholar
Voisin, Claire. Schiffer variations and the generic Torelli theorem for hypersurfaces. Compositio Math., 158(1):89122, 2022. (Cited on page 154.)Google Scholar
Šermenev, A. M.. The motif of a cubic hypersurface. Izv. Akad. Nauk SSSR Ser. Mat., 34:515522, 1970. (Cited on page 229.)Google Scholar
Wall, C. T. C.. On the orthogonal groups of unimodular quadratic forms. Math. Ann., 147:328338, 1962. (Cited on page 14.)Google Scholar
Wall, C. T. C.. Diffeomorphisms of 4-manifolds. J. London Math. Soc., 39:131140, 1964. (Cited on page 30.)Google Scholar
Wehler, Joachim. Deformation of varieties defined by sections in homogeneous vector bundles. Math. Ann., 268(4):519532, 1984. (Cited on page 216.)Google Scholar
Wei, Li and Yu, Xun. Automorphism groups of smooth cubic threefolds. J. Math. Soc. Japan, 72(4):13271343, 2020. (Cited on page 40.)Google Scholar
Weibel, Peter. Negative space: Trajectories of sculpture in the 20th and 21st centuries. Cambridge, MA: MIT Press, 2021. (Cited on page 182.)Google Scholar
Weil, André. Abstract versus classical algebraic geometry. In Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, Vol. III, pp. 550558. Amsterdam: North-Holland Publishing Co., 1956. (Cited on pages 16 and 159.)Google Scholar
Weil, André. Sur le théorème de Torelli. In Séminaire Bourbaki, Vol. 4, pp. Exp. No. 151, 207211. Paris: Soc. Math. France, 1995. (Cited on page 236.)Google Scholar
Yang, Song and Yu, Xun. Rational cubic fourfolds in Hassett divisors. C. R. Math. Acad. Sci. Paris, 358(2):129137, 2020. (Cited on pages 337 and 349.)Google Scholar
Yokoyama, Mutsumi. Stability of cubic 3-folds. Tokyo J. Math., 25(1):85105, 2002. (Cited on page 243.)Google Scholar
Yokoyama, Mutsumi. Stability of cubic hypersurfaces of dimension 4. In Higher dimensional algebraic varieties and vector bundles, RIMS Kôkyûroku Bessatsu, B9, pp. 189204. Res. Kyoto: Inst. Math. Sci. (RIMS), 2008. (Cited on pages 350 and 352.)Google Scholar
Zarhin, Yuri. Cubic surfaces and cubic threefolds, Jacobians and intermediate Jacobians. In Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II, Vol. 270 of Progr. Math., pp. 687691. Boston, MA: Birkhäuser Boston, 2009. (Cited on page 238.)Google Scholar
Zhang, Jun. Geometric compactification of moduli space of cubic surfaces and Kirwan blow-up. PhD thesis, Rice University, 2005. (Cited on page 191.)Google Scholar
Zheng, Zhiwei. Orbifold aspects of certain occult period maps. Nagoya Math. J., 243:137156, 2021. (Cited on pages 186, 190, 210, 236, 248, and 300.)Google Scholar
Zhou, Jian. Calculations of the Hirzebruch χy-genera of symmetric products by the holo-morphic Lefschetz formula. arXiv:math/9910029. (Cited on page 121.)Google Scholar
Zucker, Steven. The Hodge conjecture for cubic fourfolds. Compositio Math., 34(2):199209, 1977. (Cited on pages 254 and 309.)Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Daniel Huybrechts, Universität Bonn
  • Book: The Geometry of Cubic Hypersurfaces
  • Online publication: 15 June 2023
  • Chapter DOI: https://doi.org/10.1017/9781009280020.009
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Daniel Huybrechts, Universität Bonn
  • Book: The Geometry of Cubic Hypersurfaces
  • Online publication: 15 June 2023
  • Chapter DOI: https://doi.org/10.1017/9781009280020.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Daniel Huybrechts, Universität Bonn
  • Book: The Geometry of Cubic Hypersurfaces
  • Online publication: 15 June 2023
  • Chapter DOI: https://doi.org/10.1017/9781009280020.009
Available formats
×