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Equivalences and stratified flops

Published online by Cambridge University Press:  09 November 2011

Sabin Cautis*
Affiliation:
Department of Mathematics, Columbia University, New York, USA (email: [email protected])
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Abstract

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We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai and Atiyah flops (of type A).

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2011

References

[CK08a]Cautis, S. and Kamnitzer, J., Knot homology via derived categories of coherent sheaves I, 2 case, Duke Math. J. 142 (2008), 511588, math.AG/0701194.Google Scholar
[CK08b]Cautis, S. and Kamnitzer, J., Knot homology via derived categories of coherent sheaves II, m case, Invent. Math. 174 (2008), 165232, 0710.3216.CrossRefGoogle Scholar
[CK10]Cautis, S. and Kamnitzer, J., Braid groups and geometric categorical Lie algebra actions, arXiv:1001.0619.Google Scholar
[CKL09]Cautis, S., Kamnitzer, J. and Licata, A., Derived equivalences for cotangent bundles of Grassmannians via strong categorical 2 actions, J. Reine Angew. Math., to appear, math.AG/0902.1797.Google Scholar
[CKL11]Cautis, S., Kamnitzer, J. and Licata, A., Coherent sheaves on quiver varieties and categorification, arXiv:1104.0352.Google Scholar
[CKL10a]Cautis, S., Kamnitzer, J. and Licata, A., Categorical geometric skew Howe duality, Invent. Math. 180 (2010), 111159, math.AG/0902.1795.Google Scholar
[CKL10b]Cautis, S., Kamnitzer, J. and Licata, A., Coherent sheaves and categorical 2 actions, Duke Math. J. 154 (2010), 135179, math.AG/0902.1796.Google Scholar
[CF07]Chaput, P. E. and Fu, B., On stratified Mukai flops, Math. Res. Lett. 14 (2007), 10551067.CrossRefGoogle Scholar
[Fu07]Fu, B., Extremal contractions, stratified Mukai flops and Springer maps, Adv. Math. 213 (2007), 165182, math.AG/0605431.CrossRefGoogle Scholar
[FW08]Fu, B. and Wang, C. L., Motivic and quantum invariance under stratified Mukai flops, J. Differential Geom. 80 (2008), 261280.CrossRefGoogle Scholar
[GM03]Gelfand, S. and Manin, Y., Methods of homological algebra, second edition (Springer, 2003).CrossRefGoogle Scholar
[Huy06]Huybrechts, D., Fourier–Mukai transforms in algebraic geometry (Oxford University Press, Oxford, 2006).CrossRefGoogle Scholar
[Kaw02]Kawamata, Y., D-equivalence and K-equivalence, J. Differential Geom. 61 (2002), 147171, math.AG/0205287.CrossRefGoogle Scholar
[Kaw06]Kawamata, Y., Derived equivalence for stratified Mukai flop on 𝔾(2,4), in Mirror symmetry. V, AMS/IP Studies in Advanced Mathematics, vol. 38 (American Mathematical Society, Providence, RI, 2006), 285294, math.AG/0503101.Google Scholar
[KM08]Kollár, J. and Mori, S., Birational geometry of algebraic varieties (Cambridge University Press, Cambridge, 2008).Google Scholar
[LLW10]Lee, Y. P., Lin, H. W. and Wang, C. L., Flops, motives and invariance of the quantum rings, Ann. of Math. (2) 172 (2010), 243290, arXiv:math/0608370.CrossRefGoogle Scholar
[Mar01]Markman, E., Brill–Noether duality for moduli spaces of sheaves on K3 surfaces, J. Algebraic Geom. 10 (2001), 623694.Google Scholar
[Nam03]Namikawa, Y., Mukai flops and derived categories, J. Reine Angew. Math. 560 (2003), 6576, math.AG/0203287.Google Scholar
[Nam04]Namikawa, Y., Mukai flops and derived categories II, in Algebraic structures and moduli spaces, CRM Proceedings & Lecture Notes, vol. 38 (American Mathematical Society, Providence, RI, 2004), 149175, math.AG/0305086.Google Scholar
[Sze04]Szendröi, B., Artin group actions on derived categories of threefolds, J. Reine Angew. Math. 572 (2004), 139166, math.AG/0210121.Google Scholar