TL;DR
This paper explores the construction of derived equivalences for stratified flops in symplectic varieties, linking birational geometry, representation theory, and knot homology through categorical Lie algebra actions.
Contribution
It introduces methods to construct derived equivalences for stratified flops and explains the role of categorical Lie algebra actions in this process.
Findings
Derived equivalences can be constructed for stratified flops.
Categorical Lie algebra actions are key tools in this construction.
Connections between birational geometry, representation theory, and knot homology are elucidated.
Abstract
Stratified flops show up in the birational geometry of symplectic varieties such as resolutions of nilpotent orbits and moduli spaces of sheaves. Constructing derived equivalences between varieties related by such flops is, strangely enough, related to areas in representation theory and knot homology. In this paper we discuss how to construct such equivalences, explain the main tool for doing this (categorical Lie algebra actions) and comment on various related topics.
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