Mukai flops and P-twists

Abstract

Associated to a Mukai flop X ---> X' is on the one hand a sequence of equivalences D(X) -> D(X'), due to Kawamata and Namikawa, and on the other hand a sequence of autoequivalences of D(X), due to Huybrechts and Thomas. We work out a complete picture of the relationship between the two. We do the same for standard flops, relating Bondal and Orlov's derived equivalences to spherical twists, extending a well-known story for the Atiyah flop to higher dimensions.

26 pages. Minor changes following referee's suggestions. This is an expanded version of the paper to appear in Crelle

References in corpus (3)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
• P-functor versions of the Nakajima operators

Cited by in corpus (4)

• ${\mathbb{P}}^n$-functors
• Derived equivalences for the flops of type $C_2$ and $A_4^G$ via mutation of semiorthogonal decomposition
• Universal functors on symmetric quotient stacks of Abelian varieties
• Note on the Bondal-Orlov Functors for Toric DM Stacks