Derived categories of coherent sheaves

International Congress of Mathematicians, ICM 2006

Volumn 2, Issue , 2006, Pages 563-582

  Bridgeland, Tom ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Coherent sheaves; Derived categories

Indexed keywords

ALGEBRAIC VARIETIES; COHERENT SHEAVES; DERIVED CATEGORIES; STABILITY CONDITION; TRIANGULATED CATEGORY; UNSOLVED PROBLEMS;

EID: 33947108795     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (55)

1. Abramovich, D., and Polishchuk, A., Sheaves of t-structures and valuative criteria for stable complexes. math.AG/0309435.
2. Aspinwall, P.,A point's point of view of stringy geometry. J. High Energy Phys. 1 (2003), 002.
3. Beilinson, A., Bernstein, J., and Deligne, P., Faisceaux pervers. In Analysis and topology on singular spaces, I (Luminy, 1981)
4. Astérisque 100 (1982), 5-171.
5. Bezrukavnikov, R., and Kaledin, D., McKay equivalence for symplectic resolutions of quotient singularities. Tr. Mat. Inst. Steklova 246 (3) (2004), 20-42;
6. English transl. Proc. Steklov Inst. Math. 246 (3) (2004), 13-33
7. Bondal, A., and Orlov, D., Semiorthogonal decomposition for algebraic varieties. alggeom/9506012.
8. Bondal, A., and Orlov, D., Reconstruction of a variety from the derived category and groups of autoequivalences. Compositio Math. 125 (3) (2001), 327-344.
9. Bondal, A., and Orlov, D., Derived categories of coherent sheaves. Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. II, Higher Ed. Press, Beijing 2002, 47-56.
10. s+2,2(R) and infinite products. Invent. Math. 120 (1995), 161-213.
11. Brenner, S., and Butler, M., Generalizations of the Bernstein-Gelfand- Ponomarev reflection functors. In Representation theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math. 832, Springer-Verlag, Berlin 1980, 103-169.
12. Bridgeland, T., King, A., and Reid, M., The McKay correspondence as an equivalence of derived categories. J. Amer. Math. Soc. 14 (3) (2001), 535-554
13. Bridgeland, T., Flops and derived categories. Invent. Math. 147 (3) (2002), 613-632.
14. Bridgeland, T., Stability conditions on triangulated categories. Ann. of Math., to appear; math.AG/0212237.
15. Bridgeland, T., Stability conditions on K3 surfaces. math.AG/0307164.
16. Bridgeland, T., Stability conditions and Kleinian singularities. math.AG/0508257.
17. Chen, J.-C., Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities. J. Differential Geom. 61 (2) (2002), 227-261.
18. Craw,A., and Ishii, A., Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient. Duke Math. J. 124 (2) (2004), 259-307.
19. Douglas, M., Dirichlet branes, homological mirror symmetry, and stability. Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. III, Higher Ed. Press, Beijing 2002, 395-408.
20. Happel, D.,Reiten, I., and Smalo, S.,Tilting in abelian categories and quasitilted algebras. Mem. Amer. Math. Soc. 120, Amer. Math. Soc., Providence, RI, 1996.
21. Hille, L., and Van den Bergh, M., Fourier-Mukai transforms. math.AG/0402043.
22. Horja, R., Derived category automorphisms from mirror symmetry. Duke Math. J. 127 (1) (2005), 1-34.
23. Huybrechts, D., and Thomas, R., P-objects and autoequivalences of derived categories. Math. Res. Lett. 13 (1) (2006), 87-98.
24. Inaba, M., Toward a definition of moduli of complexes of coherent sheaves on a projective scheme. J. Math. Kyoto Univ. 42 (2) (2002), 317-329.
25. Ishii, A., and Uehara, H., Autoequivalences of derived categories on the minimal resolutions of An-singularities on surfaces. J. Differential Geom. 71 (3) (2005), 385-435.
26. Kawamata, Y., Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces. Ann. of Math. 127 (1988), 93-163.
27. Kawamata, Y., Francia's flip and derived categories. In Algebraic geometry, Walter de Gruyter, Berlin 2002, 197-215.
28. Kawamata, Y., D-equivalence and K-equivalence. J. Differential Geom. 61 (1) (2002), 147-171.
29. Kawamata, Y., Log crepant birational maps and derived categories. J. Math. Sci. Univ. Tokyo 12 (2) (2005), 211-231.
30. Kawamata,Y., Derived Categories of Toric Varieties. math.AG/0503102.
31. Kawamata, Y., Derived equivalence for stratified Mukai flop on G(2, 4). math.AG/0503101.
32. Kollár, J., Flops. Nagoya Math. J. 113 (1989), 15-36.
33. Kontsevich, M., Homological algebra of mirror symmetry. Proceedings of the International Congress of Mathematicians (Zürich, 1994), Vol. 1, Birkhäuser, Basel 1995, 120-139.
34. Kuznetsov, A., Derived categories of cubic and V14 threefolds. Tr.Mat. Inst. Steklova 246 (2004), 183-207;
35. English transl. Proc. Steklov Inst. Math. 246 (3) (2004), 171-194.
36. Kuznetsov, A., Hyperplane sections and derived categories. math.AG/0503700.
37. Kuznetsov, A., Homological Projective Duality. math.AG/0507292.
38. Kuznetsov, A., Derived Categories of Quadric Fibrations and Intersections of Quadrics. math.AG/0510670.
39. Macri, E., Some examples of moduli spaces of stability conditions on derived categories. math.AG/0411613.
40. Mukai, S.,Duality betweenD(X) andD( X̂)with its application to Picard sheaves.Nagoya Math. J. 81 (1981), 153-175.
41. Mukai, S., On the moduli space of bundles on K3 surfaces I. In Vector Bundles on Algebraic Varieties (ed. by M. F. Atiyah et al.), Tata Inst. Fund. Res. Stud. Math. 11, Oxford University Press, NewYork 1987, 341-413.
42. Namikawa, Y., Mukai flops and derived categories. J. Reine Angew. Math. 560 (2003), 65-76.
43. Namikawa,Y., Mukai flops and derived categories. II. In Algebraic structures and moduli spaces, CRM Proc. Lecture Notes 38, Amer. Math. Soc., Providence, RI, 2004, 149-175.
44. Okada, S., Stability manifold of P1. math.AG/0411220.
45. Orlov, D., Derived categories of coherent sheaves on abelian varieties and equivalences between them. Izv. Ross. Akad. Nauk Ser. Mat. 66 (3) (2002), 131-158;
46. English transl. Izv. Math. 66 (3) (2002), 569-594.
47. Reid, M., McKay correspondence. alg-geom/9702016.
48. Reid, M., La correspondance de McKay. Séminaire Bourbaki 1999/2000, Astérisque 276 (2002), 53-72.
49. Rouquier, R., Categories derivees et geometrie birationnelle. math.AG/0503548.
50. Seidel, P., and Thomas, R. P., Braid group actions on derived categories of coherent sheaves. Duke Math. J. 108 (1) (2001), 37-108, math.AG/0001043.
51. Szendröi, B., Artin group actions on derived categories of threefolds. J. Reine Angew. Math. 572 (2004), 139-166.
52. Toda,Y., Stability conditions and crepant small resolutions, preprint.
53. Toen, B., and Vaquie, M., Moduli of objects in dg-categories. math.AG/0503269.
54. Van den Bergh, M., Three-dimensional flops and noncommutative rings. Duke Math. J. 122 (3) (2004), 423-455.
55. Wierzba, J., and Wisniewski, J. A., Small contractions of symplectic 4-folds. math.AG/0201028