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4 - Introduction to stability conditions

Published online by Cambridge University Press:  05 April 2014

By
D. Huybrechts
Edited by
Leticia Brambila-Paz ,
Peter Newstead ,
Richard P. Thomas  and
Oscar García-Prada
D. Huybrechts
Affiliation:
Universität Bonn
Leticia Brambila-Paz
Affiliation:
Centro de Investigación en Matemáticas A.C. (CIMAT), Mexico
Peter Newstead
Affiliation:
University of Liverpool
Richard P. Thomas
Affiliation:
Imperial College of Science, Technology and Medicine, London
Oscar García-Prada
Affiliation:
Consejo Superior de Investigaciones Cientificas, Madrid
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Information
Moduli Spaces , pp. 179 - 229
Publisher: Cambridge University Press
Print publication year: 2014

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References

[1] D., Abramovich, A., PolishchukSheaves of t-structures and valuative criteria for stable complexes. J. Reine Angew. Math. 590 (2006), 89–130.
[2] D., AllcockCompletions, branched covers, Artin groups and singularity theory. arXiv:1106.3459v1.
[3] A., Beligiannis, I., ReitenHomological and homotopical aspects of torsion theories. Mem. AMS 188 (2007).
[4] A., Bayer, E., Macrì, Y., TodaBridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities. arXiv:1103.5010v1.
[5] A., Bayer, A., Bertram, E., Macrì, Y., TodaBridgeland stability conditions on threefolds II: An application to Fujita's conjecture. arXiv:1106.3430v1.
[6] A., Bayer, E., MacrìThe space of stability conditions on the local projective plane. Duke Math. J. 160 (2011), 263–322.
[7] A., Bondal, M., Van den BerghGenerators and representability of functors in commutative and noncommutative geometry. Moscow Math. J. 3 (2003), 1–36.
[8] C., Brav, H., ThomasBraid groups and Kleinian singularities. Math. Ann. 351 (2011), 1005–1017.
[9] T., BridgelandStability conditions on triangulated categories. Ann. of Math. 166 (2007), 317–345.
[10] T., BridgelandStability conditions on K3 surfaces. Duke Math. J. 141 (2008), 241–291.
[11] T., BridgelandSpaces of stability conditions. Algebraic geometry-Seattle 2005. Proc. Sympos. Pure Math. 80, Part 1, (2009), 1–21.
[12] T., BridgelandStability conditions on a non-compact Calabi-Yau threefold. Comm. Math. Phys. 266 (2006), 715–733.
[13] T., BridgelandStability conditions and Kleinian singularities. Int. Math. Res. Not. 21 (2009), 4142℃4157.
[14] S., DicksonA torsion theory for abelian categories. Trans. AMS 121 (1966) 223–235.
[15] S., Gelfand, Y., ManinMethods of homological algebra. Springer Monographs in Math. (2002).
[16] A., Gorodentsev, S., Kuleshov, A., Rudakovt-stabilities and t-structures on triangulated categories. Izv. Math. 68 (2004), 749–781.
[17] D., Happel, I., Reiten, S., SmaløTilting in abelian categories and quasitilted algebras. Mem. AMS 120 (1996).
[18] H., HartmannCusps of the Kâhler moduli space and stability conditions on K3 surfaces. Math. Ann. 354 (2012), 1–42.
[19] R., HartshorneResidues and duality. Springer LNM 20 (1966).
[20] D., HuybrechtsFourier-Mukai transforms in algebraic geometry. Oxford Mathematical Monographs (2006).
[21] D., Huybrechts, E., Macrì, P., StellariStability conditions for generic K3 categories. Compos. Math. 144 (2008), 134–162.
[22] D., HuybrechtsDerived and abelian equivalence of K3 surface. J. Alg. Geom. 17 (2008), 375–400.
[23] D., Huybrechts, E., Macrì, P., StellariDerived equivalences of K3 surfaces and orientation. Duke Math. J. 149 (2009), 461–507.
[24] D., HuybrechtsStability conditions via spherical objects. Math. Z. 271 (2012), 1253–1270.
[25] A., Ishii, K., Ueda, H., UeharaStability conditions on An-singularities. J. Diff. Geom. 84 (2010), 87–126.
[26] M., Kashiwara, P., SchapiraSheaves on manifolds. Grundlehren math. Wiss. 292 (1990).
[27] M., KontsevichTriangulated Categories and Geometry. Course at the École Normale Superieure (1998).
[28] M., Kontsevich, Y., SoibelmanStability structures, motivic Donaldson–Thomas invariants and cluster transformations. arXiv:0811.2435.
[29] J., Le, X.-W., ChenKaroubianness of a triangulated category. J. Alg. 310 (2007), 452–457.
[30] S., MaFourier-Mukai partners of a K3 surface and the cusps of its Kâhler moduli. Int. J. Math. 20 (2009), 727–750.
[31] E., MacrìStability conditions on curves. Math. Res. Lett. 14 (2007), 657–672.
[32] E., MacrìSome examples of spaces of stability conditions on derived categories. math.AG 0411613.
[33] E., Macrì, S., Mehrotra, P., StellariInducing stability conditions. J. Alg. Geom. 18 (2009), 605–649.
[34] S., MeinhardtStability conditions on generic complex tori. to appear in Int. J. Math.
[35] S., Meinhardt, H., PartschQuotient categories, stability conditions, and birational geometry. arXiv:0805.0492. to appear in Geometriae Dedicata.
[36] S., MukaiOn the moduli space of bundles on K3 surfaces, I. In: Vector Bundles on Algebraic Varieties, Bombay (1984), 341–413.
[37] A., NeemanTriangulated categories. Annals Math. Stud. 148 (2001).
[38] B., NoohiExplicit HRS-tilting. J. Noncommut. Geom. 3 (2009), 223–259.
[39] S., OkadaStability manifold of ℙ1. J. Alg. Geom. 15 (2006), 487–505.
[40] S., OkadaOn stability manifolds of Calabi–Yau surfaces. Int. Math. Res. Not. Article ID 58743 (2006), 1–16.
[41] A., PolishchukClassification of holomorphic vector bundles on non-commutative two-tori. Doc. Math. 9 (2004), 163–181.
[42] A., PolishchukConstant families of t-structures on derived categories of coherent sheaves. Moscow Math. J. 7 (2007), 109–134.
[43] R., ThomasStability conditions and the braid group. Comm. Anal. Geom. 14 (2006), 135–161.
[44] R., ThomasonThe classification of triangulated subcategories. Comp. Math. 105 (1997), 1–27.
[45] J.-L., VerdierDes catégories dérivées des catégories abéliennes. Astérisque 239 (1996).
[46] J., WoolfStability conditions, torsion theories and tilting. J. LMS (2) 82 (2010), 663–682.
[47] J., WoolfSome metric properties of spaces of stability conditions. arXiv:1108.2668v1

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