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Equivalences and stratified flops

  • Sabin Cautis (a1)

Abstract

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

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References

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[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.
[CK08b]Cautis, S. and Kamnitzer, J., Knot homology via derived categories of coherent sheaves II, m case, Invent. Math. 174 (2008), 165232, 0710.3216.
[CK10]Cautis, S. and Kamnitzer, J., Braid groups and geometric categorical Lie algebra actions, arXiv:1001.0619.
[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.
[CKL11]Cautis, S., Kamnitzer, J. and Licata, A., Coherent sheaves on quiver varieties and categorification, arXiv:1104.0352.
[CKL10a]Cautis, S., Kamnitzer, J. and Licata, A., Categorical geometric skew Howe duality, Invent. Math. 180 (2010), 111159, math.AG/0902.1795.
[CKL10b]Cautis, S., Kamnitzer, J. and Licata, A., Coherent sheaves and categorical 2 actions, Duke Math. J. 154 (2010), 135179, math.AG/0902.1796.
[CF07]Chaput, P. E. and Fu, B., On stratified Mukai flops, Math. Res. Lett. 14 (2007), 10551067.
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