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Window shifts, flop equivalences and Grassmannian twists

Part of: Special varieties Abelian categories (Co)homology theory

Published online by Cambridge University Press:  07 April 2014

Will Donovan  and
Ed Segal
Will Donovan
Affiliation:
The Maxwell Institute, School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK email [email protected]
Ed Segal
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK email [email protected]
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Abstract

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We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel–Thomas spherical twists, which can be seen as arising from standard flops. We first give a simple algebraic construction, which is well suited to explicit computations. We then give a geometric construction using spherical functors which we prove is equivalent.

Keywords

derived categoriesGrassmanniansderived equivalencesspherical functors

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions 18E30: Derived categories, triangulated categories 14M15: Grassmannians, Schubert varieties, flag manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 6 , June 2014 , pp. 942 - 978
Copyright
© The Author(s) 2014 

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