Window shifts, flop equivalences and Grassmannian twists. (7th April 2014)

• Record Type: Journal Article
• Authors: Donovan, Will; Segal, Ed
• Is Part Of: Compositio mathematica. Volume 150:Number 6(2014)
• Page Start: 942
• Page End: 978
• Publication Date: 2014-04-07
• Subjects: 14F05, -- 18E30 (primary), -- 14M15 (secondary); derived categories, -- Grassmannians, -- derived equivalences, -- spherical functors; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X13007641
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract: 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.