Abhyankar [1984] S., Abhyankar, “Combinatoire des tableaux de Young, variétés déterminantielles et calcul de fonctions de Hilbert”, Rend. Sem. Mat. Univ. Politec. Torino 42:3 (1984), 65–88.Google Scholar

Alexander and Hirschowitz [1995] J., Alexander and A., Hirschowitz, “Polynomial interpolation in several variables”, J. Algebraic Geom. 4:2 (1995), 201–222.Google Scholar

Altman and Kleiman [1970] A., Altman and S., Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Math. 146, Springer, Berlin-New York, 1970.Google Scholar

Aluffi [1990] P., Aluffi, “The enumerative geometry of plane cubics, I: Smooth cubics”, Trans. Amer. Math. Soc. 317:2 (1990), 501–539.Google Scholar

Aluffi [1991] P.|Aluffi, “The enumerative geometry of plane cubics, II: Nodal and cuspidal cubics”, Math. Ann. 289:4 (1991), 543–572.

Andreotti and Frankel [1959] A., Andreotti and T., Frankel, “The Lefschetz theorem on hyperplane sections”, Ann. of Math.. 2/ 69 (1959), 713–717.

Arbarello et al. [1985] E., Arbarello, M., Cornalba, P. A., Griffiths, and J., Harris, Geometry of algebraic curves, I, Grundlehren der Mathematischen Wissenschaften 267, Springer, New York, 1985.Google Scholar

Artin [1982] M., Artin, “Brauer–Severi varieties”, pp. 194–210 in Brauer groups in ring theory and algebraic geometry (Wilrijk, 1981), edited by A., Verschoren, Lecture Notes in Math. 917, Springer, Berlin-New York, 1982.Google Scholar

Atiyah [1957] M. F., Atiyah, “Complex analytic connections in fibre bundles”, Trans. Amer. Math. Soc. 85 (1957), 181–207.Google Scholar

Atiyah and Hirzebruch [1961] M. F., Atiyah and F., Hirzebruch, “Vector bundles and homogeneous spaces”, pp. 7–38 in Differential Geometry, edited by C. B., Allendoerfer, Proc. Sympos. Pure Math. 3, Amer. Math. Soc., Providence, RI, 1961.Google Scholar

Bădescu [2001] L., Bădescu, Algebraic surfaces, Springer, New York, 2001.Google Scholar

Barth [1975] W., Barth, “Larsen's theorem on the homotopy groups of projective manifolds of small embedding codimension”, pp. 307–313 in Algebraic geometry (Arcata, CA, 1974), edited by R., Hartshorne, Proc. Sympos. Pure Math. 29, Amer. Math. Soc., Providence, RI, 1975.Google Scholar

Barth [1977] W., Barth, “Moduli of vector bundles on the projective plane”, Invent. Math. 42 (1977), 63–91.Google Scholar

Barth et al. [2004] W., Barth, K., Hulek, C. A. M., Peters, and A. Van de, Ven, Compact complex surfaces, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 4, Springer, Berlin, 2004.Google Scholar

Bayer [1982] D., Bayer, The division algorithm and the Hilbert scheme, Ph.D. thesis, Harvard University, Ann Arbor, MI, 1982. Available at http://search.proquest.com/docview/303209159.Google Scholar

Bayer and Eisenbud [1995] D., Bayer and D., Eisenbud, “Ribbons and their canonical embeddings”, Trans. Amer. Math. Soc. 347:3 (1995), 719–756.Google Scholar

Beauville [1996] A., Beauville, Complex algebraic surfaces, 2nd ed., London Mathematical Society Student Texts 34, Cambridge University Press, 1996.Google Scholar

Beheshti [2006] R., Beheshti, “Lines on projective hypersurfaces”, J. Reine Angew. Math. 592 (2006), 1–21.Google Scholar

Beheshti and Mohan Kumar [2013] R., Beheshti and N., Mohan Kumar, “Spaces of rational curves on hypersurfaces”, J. Ramanujan Math. Soc.28A (2013), 1–19.Google Scholar

Bifet et al. [1990] E., Bifet, C. De, Concini, and C., Procesi, “Cohomology of regular embeddings”, Adv. Math. 82:1 (1990), 1–34.

Boissière and Sarti [2007] S., Boissière and A., Sarti, “Counting lines on surfaces”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6:1 (2007), 39–52.Google Scholar

Borel [1991] A., Borel, Linear algebraic groups, 2nd ed., Graduate Texts in Mathematics 126, Springer, New York, 1991.

Borel and Serre [1958] A.|Borel and J.-P., Serre, “Le théorème de Riemann–Roch”, Bull. Soc. Math. France 86 (1958), 97–136.Google Scholar

Bott and Tu [1982] R., Bott and L. W., Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer, New York-Berlin, 1982.Google Scholar

Brambilla and Ottaviani [2008] M. C., Brambilla and G., Ottaviani, “On the Alexander–Hirschowitz theorem”, J. Pure Appl. Algebra 212:5 (2008), 1229–1251.Google Scholar

Brieskorn and Knörrer [1986] E., Brieskorn and H., Knörrer, Plane algebraic curves, Birkhäuser, Basel, 1986.Google Scholar

Brill and Noether [1874] A., Brill and M., Noether, “Über die algebraischen Functionen und ihre Anwendung in der Geometrie”, Math. Ann. 7 (1874), 269–310.Google Scholar

Buchsbaum and Eisenbud [1977] D. A., Buchsbaum and D., Eisenbud, “What annihilates a module?”, J. Algebra 47:2 (1977), 231–243.Google Scholar

Call and Lyubeznik [1994] F., Call and G., Lyubeznik, “A simple proof of Grothendieck's theorem on the parafactoriality of local rings”, pp. 15–18 in Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), edited by W. J., Heinzer et al., Contemp. Math. 159, Amer. Math. Soc., Providence, RI, 1994.Google Scholar

Caporaso and Harris [1998] L., Caporaso and J., Harris, “Counting plane curves of any genus”, Invent. Math. 131:2 (1998), 345–392.Google Scholar

Cavazzani [2016] F., Cavazzani, A geometric invariant theory compactification of the space of twisted cubics, Ph.D. thesis, Harvard University, 2016.Google Scholar

Ceresa and Collino [1983] G., Ceresa and A., Collino, “Some remarks on algebraic equivalence of cycles”, Pacific J. Math. 105:2 (1983), 285–290.Google Scholar

Chasles [1864] M., Chasles, “Construction des coniques qui satisfont à cinque conditions”, C. R. Acad. Sci. Paris 58 (1864), 297–308.Google Scholar

Chern [1946] S.-S., Chern, “Characteristic classes of Hermitian manifolds”, Ann. of Math. (2) 47 (1946), 85–121.Google Scholar

Chow [1956] W.-L., Chow, “On equivalence classes of cycles in an algebraic variety”, Ann. of Math. (2) 64 (1956), 450–479.Google Scholar

Ciliberto [1987] C., Ciliberto, “Hilbert functions of finite sets of points and the genus of a curve in a projective space”, pp. 24–73 in Space curves (Rocca di Papa, 1985), edited by F., Ghione et al., Lecture Notes in Math. 1266, Springer, Berlin, 1987.Google Scholar

Clebsch [1861] A., Clebsch, “Zur Theorie der algebraischen Flächen”, J. Reine Angew. Math. 58 (1861), 93–108.Google Scholar

Coșkun [2009] I., Coșkun, “A Littlewood–Richardson rule for two-step flag varieties”, Invent. Math. 176:2 (2009), 325–395.Google Scholar

Collino [1975] A., Collino, “The rational equivalence ring of symmetric products of curves”, Illinois J. Math. 19:4 (1975), 567–583.Google Scholar

Cools et al. [2012] F., Cools, J., Draisma, S., Payne, and E., Robeva, “A tropical proof of the Brill–Noether theorem”, Adv. Math. 230:2 (2012), 759–776.Google Scholar

Cox and Katz [1999] D. A., Cox and S., Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs 68, Amer. Math. Soc., Providence, RI, 1999.Google Scholar

Dale [1985] M., Dale, “Severi's theorem on the Veronese-surface”, J. London Math. Soc. (2) 32:3 (1985), 419–425.Google Scholar

De Concini and Procesi [1983] C. De, Concini and C., Procesi, “Complete symmetric varieties”, pp. 1–44 in Invariant theory (Montecatini, 1982), edited by F., Gherardelli, Lecture Notes in Math. 996, Springer, Berlin, 1983.Google Scholar

De Concini and Procesi [1985] C. De, Concini and C., Procesi, “Complete symmetric varieties, II: Intersection theory”, pp. 481–513 in Algebraic groups and related topics (Kyoto/Nagoya, 1983), edited by R., Hotta, Adv. Stud. Pure Math. 6, North-Holland, Amsterdam, 1985.Google Scholar

De Concini et al. [1980] C. De, Concini, D., Eisenbud, and C., Procesi, “Young diagrams and determinantal varieties”, Invent. Math. 56:2 (1980), 129–165.Google Scholar

De Concini et al. [1982] C. De, Concini, D., Eisenbud, and C., Procesi, Hodge algebras, Astérisque 91, Société Mathématique de France, Paris, 1982.Google Scholar

De Concini et al. [1988] C. De, Concini, M., Goresky, R., MacPherson, and C., Procesi, “On the geometry of quadrics and their degenerations”, Comment. Math. Helv. 63:3 (1988), 337–413.Google Scholar

Decker et al. [2015] W., Decker, G.-M., Greuel, G., Pfister, and H., Schönemann, “SINGULAR 4-0-2—A computer algebra system for polynomial computations”, 2015. Available at http://singular.uni-kl.de.

Dieudonné [1969] J., Dieudonné, “Algebraic geometry”, Advances in Math. 3 (1969), 233–321.Google Scholar

Donagi and Smith [1980] R., Donagi and R., Smith, “The degree of the Prym map onto the moduli space of five-dimensional abelian varieties”, pp. 143–155 in Journées de Géometrie Algébrique d'Angers (Angers, 1979), edited by A., Beauville, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.Google Scholar

Doubilet et al. [1974] P., Doubilet, G.-C., Rota, and J., Stein, “On the foundations of combinatorial theory, IX: Combinatorial methods in invariant theory”, Studies in Appl. Math. 53 (1974), 185–216.Google Scholar

Ein [1986] L., Ein, “Varieties with small dual varieties, I”, Invent. Math. 86:1 (1986), 63–74.Google Scholar

Eisenbud [1995] D., Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics 150, Springer, New York, 1995.Google Scholar

Eisenbud [2005] D., Eisenbud, The geometry of syzygies, Graduate Texts in Mathematics 229, Springer, New York, 2005.Google Scholar

Eisenbud and Harris [1983a] D., Eisenbud and J., Harris, “Divisors on general curves and cuspidal rational curves”, Invent. Math. 74:3 (1983), 371–418.Google Scholar

Eisenbud and Harris [1983b] D., Eisenbud and J., Harris, “A simpler proof of the Gieseker–Petri theorem on special divisors”, Invent. Math. 74:2 (1983), 269–280.Google Scholar

Eisenbud and Harris [1987] D., Eisenbud and J., Harris, “On varieties of minimal degree (a centennial account)”, pp. 3–13 in Algebraic geometry (Bowdoin, ME, 1985), edited by S. J., Bloch, Proc. Sympos. Pure Math. 46, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

Eisenbud and Harris [1992] D., Eisenbud and J., Harris, “Finite projective schemes in linearly general position”, J. Algebraic Geom. 1:1 (1992), 15–30.Google Scholar

Eisenbud and Harris [2000] D., Eisenbud and J., Harris, The geometry of schemes, Graduate Texts in Mathematics 197, Springer, New York, 2000.Google Scholar

Eisenbud and Schreyer [2008] D., Eisenbud and F.-O., Schreyer, “Relative Beilinson monad and direct image for families of coherent sheaves”, Trans. Amer. Math. Soc. 360:10 (2008), 5367–5396.Google Scholar

Eisenbud et al. [1996] D., Eisenbud, M., Green, and J., Harris, “Cayley–Bacharach theorems and conjectures”, Bull. Amer. Math. Soc. (N.S.) 33:3 (1996), 295–324.Google Scholar

Eisenbud et al. [2003] D., Eisenbud, F.-O., Schreyer, and J., Weyman, “Resultants and Chow forms via exterior syzygies”, J. Amer. Math. Soc. 16:3 (2003), 537–579.Google Scholar

Fröberg [1985] R., Fröberg, “An inequality for Hilbert series of graded algebras”, Math. Scand. 56:2 (1985), 117–144.Google Scholar

Fulton [1984] W., Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 2, Springer, Berlin, 1984.Google Scholar

Fulton [1993] W., Fulton, Introduction to toric varieties, Annals of Mathematics Studies 131, Princeton University Press, 1993.Google Scholar

Fulton [1997] W., Fulton, Young tableaux, London Mathematical Society Student Texts 35, Cambridge University Press, 1997.Google Scholar

Fulton and Harris [1991] W., Fulton and J., Harris, Representation theory, Graduate Texts in Mathematics 129, Springer, New York, 1991.Google Scholar

Fulton and Lazarsfeld [1981] W., Fulton and R., Lazarsfeld, “On the connectedness of degeneracy loci and special divisors”, Acta Math. 146:3-4 (1981), 271–283.Google Scholar

Fulton and MacPherson [1978] W., Fulton and R., MacPherson, “Defining algebraic intersections”, pp. 1– 30 in Algebraic geometry (Univ. Tromso, 1977), edited by L. D., Olson, Lecture Notes in Math. 687, Springer, Berlin, 1978.Google Scholar

Fulton and MacPherson [1981] W., Fulton and R., MacPherson, Categorical framework for the study of singular spaces, Mem. Amer. Math. Soc. 243, Amer. Math. Soc., Providence, RI, 1981.Google Scholar

Fulton and Pandharipande [1997] W., Fulton and R., Pandharipande, “Notes on stable maps and quantum cohomology”, pp. 45–96 in Algebraic geometry (Santa Cruz, 1995), edited by J., Kollár et al., Proc. Sympos. Pure Math. 62, Amer. Math. Soc., Providence, RI, 1997.Google Scholar

Fulton et al. [1983] W., Fulton, S., Kleiman, and R., MacPherson, “About the enumeration of contacts”, pp. 156–196 in Algebraic geometry—open problems (Ravello, 1982), edited by C., Ciliberto et al., Lecture Notes in Math. 997, Springer, Berlin, 1983. van Gastel [1990] L. van, Gastel, “Excess intersections in projective space”, pp. 109–124 in Topics in algebra, II (Warsaw, 1988), edited by S., Balcerzyk et al., Banach Center Publ. 26, PWN, Warsaw, 1990.Google Scholar

Gelfand et al. [2008] I. M., Gelfand, M. M., Kapranov, and A. V., Zelevinsky, Discriminants, resultants and multidimensional determinants, Birkhäuser, Boston, 2008. Reprint of the 1994 edition.Google Scholar

Golubitsky and Guillemin [1973] M., Golubitsky and V., Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics 14, Springer, New York-Heidelberg, 1973.Google Scholar

Grayson and Stillman [2015] D., Grayson and M., Stillman, “Macaulay2: a software system for research in algebraic geometry”, 2015. Available at http://math.uiuc.edu/Macaulay2.

Grayson et al. [2012] D., Grayson, A., Seceleanu, and M., Stillman, “Computations in intersection rings of flag bundles”, preprint, 2012. Available at http://arxiv.org/abs/1205.4190.

Green [1989] M., Green, “Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann”, pp. 76–86 in Algebraic curves and projective geometry (Trento, 1988), edited by E., Ballico and C., Ciliberto, Lecture Notes in Math. 1389, Springer, Berlin, 1989.Google Scholar

Greuel et al. [2007] G.-M., Greuel, C., Lossen, and E., Shustin, Introduction to singularities and deformations, Springer, Berlin, 2007.Google Scholar

Griffiths and Adams [1974] P., Griffiths and J., Adams, Topics in algebraic and analytic geometry, Mathematical Notes 13, Princeton University Press and University of Tokyo Press, 1974.Google Scholar

Griffiths and Harris [1979] P., Griffiths and J., Harris, “Algebraic geometry and local differential geometry”, Ann. Sci. École Norm. Sup. (4) 12:3 (1979), 355–452.Google Scholar

Griffiths and Harris [1980] P., Griffiths and J., Harris, “On the variety of special linear systems on a general algebraic curve”, Duke Math. J. 47:1 (1980), 233–272.Google Scholar

Griffiths and Harris [1985] P., Griffiths and J., Harris, “On the Noether–Lefschetz theorem and some remarks on codimension-two cycles”, Math. Ann. 271:1 (1985), 31–51.Google Scholar

Griffiths and Harris [1994] P., Griffiths and J., Harris, Principles of algebraic geometry, Wiley, New York, 1994. Reprint of the 1978 original.

Grothendieck [1958] A., Grothendieck, “La théorie des classes de Chern”, Bull. Soc. Math. France 86 (1958), 137–154.Google Scholar

Grothendieck [1963] A., Grothendieck, “Eléments de géométrie algébrique, III: Étude cohomologique des faisceaux cohÉrents, II”, Inst. Hautes Études Sci. Publ. Math. 17 (1963), 5–91.Google Scholar

Grothendieck [1966a] A., Grothendieck, “Le groupe de Brauer, I: Algèbres d'Azumaya et interprétations diverses”, in Séminaire Bourbaki 1964=1965 (Exposé 290), W. A., Benjamin, Amsterdam, 1966. Reprinted as pp. 199–219 in Séminaire Bourbaki 9, Soc. Math. France, Paris, 1995.Google Scholar

Grothendieck [1966b] A., Grothendieck, “Techniques de construction et théorèmes d'existence en géométrie algébrique, IV: Les schémas de Hilbert”, in Séminaire Bourbaki 1960=1961 (Exposé 221), W. A., Benjamin, Amsterdam, 1966. Reprinted as pp. 249–276 in Séminaire Bourbaki 6, Soc. Math. France, Paris, 1995.

Gruson and Peskine [1982] L., Gruson and C., Peskine, “Genre des courbes de l'espace projectif, II”, Ann. Sci. École Norm. Sup. (4) 15:3 (1982), 401–418.Google Scholar

Hamm [1995] H. A., Hamm, “Affine varieties and Lefschetz theorems”, pp. 248–262 in Singularity theory (Trieste, 1991), edited by D. T., Lê et al., World Sci. Publ., 1995.

Harris [1979] J., Harris, “Galois groups of enumerative problems”, Duke Math. J. 46:4 (1979), 685–724.Google Scholar

Harris [1982] J., Harris, “Theta-characteristics on algebraic curves”, Trans. Amer. Math. Soc. 271:2 (1982), 611–638.Google Scholar

Harris [1995] J., Harris, Algebraic geometry, Graduate Texts in Mathematics 133, Springer, New York, 1995. Corrected reprint of the 1992 original.Google Scholar

Harris and Eisenbud [1982] J., Harris and D., Eisenbud, Curves in projective space, Séminaire de Mathématiques Supérieures 85, Presses de l'Université de Montréal, Quebec, Canada, 1982.Google Scholar

Harris and Morrison [1998] J., Harris and I., Morrison, Moduli of curves, Graduate Texts in Mathematics 187, Springer, New York, 1998.Google Scholar

Harris et al. [1998] J., Harris, B., Mazur, and R., Pandharipande, “Hypersurfaces of low degree”, Duke Math. J. 95:1 (1998), 125–160.Google Scholar

Hartshorne [1966] R., Hartshorne, “Connectedness of the Hilbert scheme”, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 5–48.Google Scholar

Hartshorne [1974] R., Hartshorne, “Varieties of small codimension in projective space”, Bull. Amer. Math. Soc. 80 (1974), 1017–1032.Google Scholar

Hartshorne [1977] R., Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer, New York-Heidelberg, 1977.Google Scholar

Hassett [2007] B., Hassett, Introduction to algebraic geometry, Cambridge University Press, 2007.Google Scholar

Herzog and Trung [1992] J., Herzog and N. V., Trung, “Gröbner bases and multiplicity of determinantal and Pfaffian ideals”, Adv. Math. 96:1 (1992), 1–37.Google Scholar

Hironaka [1975] H., Hironaka, “Triangulations of algebraic sets”, pp. 165–185 in Algebraic geometry (Arcata, CA, 1974), edited by R., Hartshorne, Proc. Sympos. Pure Math. 29, Amer. Math. Soc., Providence, RI, 1975.Google Scholar

Hirzebruch [1966] F., Hirzebruch, Topological methods in algebraic geometry, 3rd ed., Grundlehren der Mathematischen Wissenschaften 131, Springer, New York, 1966.Google Scholar

Hochster [1973] M., Hochster, “Grassmannians and their Schubert subvarieties are arithmetically Cohen– Macaulay”, J. Algebra 25 (1973), 40–57.Google Scholar

Hochster [1977] M., Hochster, “The Zariski–Lipman conjecture in the graded case”, J. Algebra 47:2 (1977), 411–424.Google Scholar

Hochster and Laksov [1987] M., Hochster and D., Laksov, “The linear syzygies of generic forms”, Comm. Algebra 15:1-2 (1987), 227–239.Google Scholar

Hodge [1943] W. V. D., Hodge, “Some enumerative results in the theory of forms”, Proc. Cambridge Philos. Soc. 39 (1943), 22–30.Google Scholar

Hodge and Pedoe [1952] W. V. D., Hodge and D., Pedoe, Methods of algebraic geometry, II, Cambridge University Press, 1952.Google Scholar

Hoyt [1971] W. L.|Hoyt, “On the moving lemma for rational equivalence”, J. Indian Math. Soc. (N.S.) 35 (1971), 47–66.

Hulek [1979] K., Hulek, “Stable rank-2 vector bundles on P2 with c1 odd”, Math. Ann. 242:3 (1979), 241–266.Google Scholar

Hulek [2012] K., Hulek, Elementare algebraische Geometrie, 2nd ed., Springer Spektrum, Wiesbaden, 2012.Google Scholar

Illusie [1972] L., Illusie, Complexe cotangent et déformations, II, Lecture Notes in Math. 283, Springer, Berlin-New York, 1972.Google Scholar

Kempf [1971] G., Kempf, “Schubert methods with an application to algebraic curves”, Publ. Math Centrum 6 (1971).Google Scholar

Kempf and Laksov [1974] G., Kempf and D., Laksov, “The determinantal formula of Schubert calculus”, Acta Math. 132 (1974), 153–162.Google Scholar

Kleiman [1974] S. L., Kleiman, “The transversality of a general translate”, Compositio Math. 28 (1974), 287–297.Google Scholar

Kleiman [1976] S. L., Kleiman, “r-special subschemes and an argument of Severi's”, Advances in Math. 22:1 (1976), 1–31.Google Scholar

Kleiman [1984] S. L., Kleiman, “About the conormal scheme”, pp. 161–197 in Complete intersections (Acireale, 1983), edited by S., Greco and R., Strano, Lecture Notes in Math. 1092, Springer, Berlin, 1984.

Kleiman [1986] S. L., Kleiman, “Tangency and duality”, pp. 163–225 in Proceedings of the 1984 Vancouver conference in algebraic geometry, edited by J., Carrell et al., CMS Conf. Proc. 6, Amer. Math. Soc., Providence, RI, 1986.Google Scholar

Kleiman and Laksov [1972] S. L., Kleiman and D., Laksov, “On the existence of special divisors”, Amer. J. Math. 94 (1972), 431–436.Google Scholar

Kleiman and Laksov [1974] S. L., Kleiman and D., Laksov, “Another proof of the existence of special divisors”, Acta Math. 132 (1974), 163–176.Google Scholar

Kleiman and Speiser [1991] S. L., Kleiman and R., Speiser, “Enumerative geometry of nonsingular plane cubics”, pp. 85–113 in Algebraic geometry (Sundance 1988), edited by B., Harbourne and R., Speiser, Contemp. Math. 116, Amer. Math. Soc., Providence, RI, 1991.Google Scholar

Laksov [1987] D., Laksov, “Completed quadrics and linear maps”, pp. 371–387 in Algebraic geometry (Bowdoin, ME, 1985), edited by S. J., Bloch, Proc. Sympos. Pure Math. 46, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

Landsberg [2012] J. M., Landsberg, Tensors: geometry and applications, Graduate Studies in Mathematics 128, Amer. Math. Soc., Providence, RI, 2012.Google Scholar

Larsen [1973] M. E., Larsen, “On the topology of complex projective manifolds”, Invent. Math. 19 (1973), 251–260.Google Scholar

Lazarsfeld [1986] R., Lazarsfeld, “Brill–Noether–Petri without degenerations”, J. Differential Geom. 23:3 (1986), 299–307.Google Scholar

Lazarsfeld [1994] R., Lazarsfeld, “Lectures on Linear Series”, lecture notes, 1994. Available at http://arxiv.org/abs/alg-geom/9408011.

Lefschetz [1950] S., Lefschetz, L'analysis situs et la géométrie algébrique, Gauthier-Villars, Paris, 1950.Google Scholar

Lipman [1965] J., Lipman, “Free derivation modules on algebraic varieties”, Amer. J. Math. 87 (1965), 874–898.Google Scholar

Lojasiewicz [1964] S., Lojasiewicz, “Triangulation of semi-analytic sets”, Ann. Scuola Norm. Sup. Pisa (3) 18 (1964), 449–474.Google Scholar

Manin [1986] Y. I., Manin, Cubic forms, 2nd ed., North-Holland Mathematical Library 4, North-Holland, Amsterdam, 1986.Google Scholar

Maruyama [1983] M., Maruyama, “Singularities of the curve of jumping lines of a vector bundle of rank 2 on P2”, pp. 370–411 in Algebraic geometry (Tokyo/Kyoto, 1982), edited by M., Raynaud and T., Shioda, Lecture Notes in Math. 1016, Springer, Berlin, 1983.Google Scholar

Mather [1971] J. N., Mather, “Stability of C∞ mappings, VI: The nice dimensions”, pp. 207–253 in Singularities—Symposium I (Univ. Liverpool, 1969/70), edited by C. T. C., Wall, Lecture Notes in Math. 192, Springer, Berlin, 1971.Google Scholar

Mather [1973] J. N., Mather, “Generic projections”, Ann. of Math. (2) 98 (1973), 226–245.Google Scholar

Matsumura [2014] S.-I., Matsumura, “Weak Lefschetz theorems and the topology of zero loci of ample vector bundles”, Comm. Anal. Geom. 22:4 (2014), 595–616.Google Scholar

McCrory and Shifrin [1984] C., McCrory and T., Shifrin, “Cusps of the projective Gauss map”, J. Differential Geom. 19:1 (1984), 257–276.Google Scholar

Milne [2008] J. S., Milne, “Abelian varieties (v2.00)”, notes, 2008. Available at http://jmilne.org/math/CourseNotes/AV.pdf.

Milnor [1963] J., Milnor, Morse theory, Annals of Mathematics Studies 51, Princeton University Press, 1963.Google Scholar

Milnor [1965] J., Milnor, Topology from the differentiable viewpoint, The University Press of Virginia, Charlottesville, VA, 1965.Google Scholar

Milnor [1997] J., Milnor, Topology from the differentiable viewpoint, Princeton University Press, 1997. Revised reprint of the 1965 original.Google Scholar

Morrison [1993] D. R., Morrison, “Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians”, J. Amer. Math. Soc. 6:1 (1993), 223–247.Google Scholar

Mumford [1962] D., Mumford, “Further pathologies in algebraic geometry”, Amer. J. Math. 84 (1962), 642–648.Google Scholar

Mumford [1966] D., Mumford, Lectures on curves on an algebraic surface, Annals of Mathematics Studies 59, Princeton University Press, 1966.Google Scholar

Mumford [1976] D., Mumford, Algebraic geometry, I: Complex projective varieties, Grundlehren der Mathematischen Wissenschaften 221, Springer, Berlin-New York, 1976.Google Scholar

Mumford [1983] D., Mumford, “Towards an enumerative geometry of the moduli space of curves”, pp. 271–328 in Arithmetic and geometry, II, edited by M., Artin and J., Tate, Progr. Math. 36, Birkhäuser, Boston, 1983.Google Scholar

Mumford [2008] D., Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5, Hindustan Book Agency, New Delhi, 2008. Corrected reprint of the 1974 edition.Google Scholar

Okonek [1987] C., Okonek, “Barth–Lefschetz theorems for singular spaces”, J. Reine Angew. Math. 374 (1987), 24–38.Google Scholar

Palais [1965] R. S., Palais (editor), Seminar on the Atiyah–Singer index theorem, Annals of Mathematics Studies 57, Princeton University Press, 1965.Google Scholar

Pardue [1996] K., Pardue, “Deformation classes of graded modules and maximal Betti numbers”, Illinois J. Math. 40:4 (1996), 564–585.Google Scholar

Peeva and Stillman [2005] I., Peeva and M., Stillman, “Connectedness of Hilbert schemes”, J. Algebraic Geom. 14:2 (2005), 193–211.Google Scholar

Perkinson [1996] D., Perkinson, “Principal parts of line bundles on toric varieties”, Compositio Math. 104:1 (1996), 27–39.Google Scholar

Peskine and Szpiro [1974] C., Peskine and L., Szpiro, “Liaison des variétés algébriques, I”, Invent. Math. 26 (1974), 271–302.Google Scholar

Piene and Schlessinger [1985] R., Piene and M., Schlessinger, “On the Hilbert scheme compactification of the space of twisted cubics”, Amer. J. Math. 107:4 (1985), 761–774.Google Scholar

Porteous [1971] I. R., Porteous, “Simple singularities of maps”, pp. 286–307 in Singularities—Symposium I (Univ. Liverpool, 1969/70), edited by C. T. C., Wall, Lecture Notes in Math. 192, Springer, Berlin, 1971.Google Scholar

Ran [2005a] Z., Ran, “Geometry on nodal curves”, Compos. Math. 141:5 (2005), 1191–1212.Google Scholar

Ran [2005b] Z., Ran, “A note on Hilbert schemes of nodal curves”, J. Algebra 292:2 (2005), 429–446.Google Scholar

Re [2012] R., Re, “Principal parts bundles on projective spaces and quiver representations”, Rend. Circ. Mat. Palermo (2) 61:2 (2012), 179–198.Google Scholar

Reeves [1995] A. A., Reeves, “The radius of the Hilbert scheme”, J. Algebraic Geom. 4:4 (1995), 639–657.Google Scholar

Reid [1988] M., Reid, Undergraduate algebraic geometry, London Mathematical Society Student Texts 12, Cambridge University Press, 1988.Google Scholar

Riedl and Yang [2014] E., Riedl and D., Yang, “Kontsevich spaces of rational curves on Fano hypersurfaces”, preprint, 2014. Available at http://arxiv.org/abs/1409.3802.

Roberts [1972a] J., Roberts, “Chow's moving lemma”, pp. 89–96 in Algebraic geometry (Fifth Nordic Summer School, Oslo, 1970), edited by F., Oort, Wolters-Noordhoff, Groningen, 1972. Appendix 2 to “Motives”, by Steven L., Kleiman, pp. 53–82 of the same reference.

Roberts [1972b] J., Roberts, “The variation of singular cycles in an algebraic family of morphisms”, Trans. Amer. Math. Soc. 168 (1972), 153–164.Google Scholar

Russell [2003] H., Russell, “Counting singular plane curves via Hilbert schemes”, Adv. Math. 179:1 (2003), 38–58.Google Scholar

Samuel [1956] P., Samuel, “Rational equivalence of arbitrary cycles”, Amer. J. Math. 78 (1956), 383–400.Google Scholar

Samuel [1971] P., Samuel, “Séminaire sur l'équivalence rationnelle”, pp. 1–17 in Séminaire sur l'équivalence rationnelle (Paris-Orsay, 1971), edited by M., Flexor and J.-J., Risler, Publ. Math. Orsay 425, Dép. Math. Fac. Sci., Univ. Paris, Orsay, 1971.Google Scholar

Schubert [1979] H., Schubert, Kalkül der abzählenden Geometrie, Springer, Berlin-New York, 1979. Reprint of the 1879 original.Google Scholar

Segre [1943] B., Segre, “The maximum number of lines lying on a quartic surface”, Quart. J. Math., Oxford Ser. 14 (1943), 86–96.Google Scholar

Serre [1955] J.-P., Serre, “Faisceaux algébriques cohérents”, Ann. of Math. (2) 61 (1955), 197–278.Google Scholar

Serre [1955/1956] J.-P., Serre, “Géométrie algébrique et géométrie analytique”, Ann. Inst. Fourier, Grenoble 6 (1955/1956), 1–42.Google Scholar

Serre [1979] J.-P., Serre, Local fields, Graduate Texts in Mathematics 67, Springer, New York-Berlin, 1979.

Serre [2000] J.-P., Serre, Local algebra, Springer, Berlin, 2000.Google Scholar

Seshadri [2007] C. S., Seshadri, Introduction to the theory of standard monomials, Texts and Readings in Mathematics 46, Hindustan Book Agency, New Delhi, 2007. Revised reprint of the 1985 original.Google Scholar

Severi [1933] F., Severi, “Über die grundlagen der algebraischen Geometrie”, Abh. Math. Sem. Univ. Hamburg 9:1 (1933), 335–364.Google Scholar

Shafarevich [1994] I. R., Shafarevich, Basic algebraic geometry, I, 2nd ed., Springer, Berlin, 1994.Google Scholar

Smith [2000] G. G., Smith, “Computing global extension modules”, J. Symbolic Comput. 29:4-5 (2000), 729–746.Google Scholar

Smith et al. [2000] K. E., Smith, L., Kahanpää, P., Kekäläinen, and W., Traves, An invitation to algebraic geometry, Springer, New York, 2000.Google Scholar

Srinivas [2010] V., Srinivas, “Algebraic cycles on singular varieties”, pp. 603–623 in Proceedings of the International Congress of Mathematicians, II, edited by R., Bhatia et al., Hindustan Book Agency, New Delhi, 2010.Google Scholar

Stacks Project [2015] T. Stacks, Project, “Stacks Project”, 2015. Available at http://stacks.math.columbia.edu.

Stanley [1999] R. P., Stanley, Enumerative combinatorics, II, Cambridge Studies in Advanced Mathematics 62, Cambridge University Press, 1999.Google Scholar

Steiner [1848] J., Steiner, “Elementare Lösung einer geometrischen Aufgabe, und über einige damit in Beziehung stehende Eigenschaften der Kegelschnitte”, J. Reine Angew. Math. 37 (1848), 161–192.Google Scholar

Teissier [1977] B., Teissier, “The hunting of invariants in the geometry of discriminants”, pp. 565–678 in Real and complex singularities (Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), edited by P., Holm, Sijthoff & Noordhoff, Alphen aan den Rijn, 1977.Google Scholar

Terracini [1911] A., Terracini, “Sulle Vk per cui la varietà degli Sh.h (C)-seganti ha dimensione minore dell'ordinario”, Rend. Circ. Mat. Palermo 31 (1911), 392–396.Google Scholar

Totaro [2013] B., Totaro, “On the integral Hodge and Tate conjectures over a number field”, Forum Math. Sigma 1 (2013), e4, 13 pp.Google Scholar

Totaro [2014] B., Totaro, “Chow groups, Chow cohomology, and linear varieties”, Forum Math. Sigma 2 (2014), e17, 25 pp.Google Scholar

Vakil [2006a] R., Vakil, “A geometric Littlewood–Richardson rule”, Ann. of Math. (2) 164:2 (2006), 371–421.Google Scholar

Vakil [2006b] R., Vakil, “Murphy's law in algebraic geometry: badly-behaved deformation spaces”, Invent. Math. 164:3 (2006), 569–590.Google Scholar

Vogel [1984] W., Vogel, Lectures on results on Bezout's theorem, Tata Institute of Fundamental Research Lectures on Mathematics and Physics 74, Springer, Berlin, 1984.Google Scholar

Voloch [2003] J. F., Voloch, “Surfaces in ℙ3 over finite fields”, pp. 219–226 in Topics in algebraic and noncommutative geometry (Luminy/Annapolis, MD, 2001), edited by C. G., Melles et al., Contemp. Math. 324, Amer. Math. Soc., Providence, RI, 2003.

Whitney [1941] H., Whitney, “On the topology of differentiable manifolds”, pp. 101–141 in Lectures in Topology, edited by R., Wilder and W., Ayres, University of Michigan Press, Ann Arbor, MI, 1941.

Zak [1991] F. L., Zak, “Some properties of dual varieties and their applications in projective geometry”, pp. 273–280 in Algebraic geometry (Chicago, IL, 1989), edited by S., Bloch et al., Lecture Notes in Math. 1479, Springer, Berlin, 1991.Google Scholar

Zariski [1982] O., Zariski, “Dimension-theoretic characterization of maximal irreducible algebraic systems of plane nodal curves of a given order n and with a given number d of nodes”, Amer. J. Math. 104:1 (1982), 209–226.Google Scholar