Mukai flops and P-twists
N. Addington, W. Donovan, C. Meachan
TL;DR
This paper explores the relationships between derived equivalences and autoequivalences in the context of Mukai flops and standard flops, extending known results to higher dimensions.
Contribution
It provides a comprehensive analysis of how derived equivalences relate to autoequivalences for Mukai and standard flops, generalizing existing theories to higher dimensions.
Findings
Complete characterization of derived equivalences and autoequivalences for Mukai flops.
Extension of the Atiyah flop story to higher dimensions.
Connections between Bondal-Orlov equivalences and spherical 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.
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