Equivariant Matrix Factorizations and Hamiltonian reduction

TL;DR

This paper establishes an equivalence between categories of G-equivariant coherent sheaves on the derived fiber of the moment map and G-equivariant matrix factorizations with a potential, advancing the understanding of Hamiltonian reduction in algebraic geometry.

Contribution

It introduces a new categorical equivalence connecting derived categories of sheaves and matrix factorizations in the context of Hamiltonian reduction.

Findings

Proves an equivalence of categories related to the moment map

Bridges coherent sheaves and matrix factorizations in Hamiltonian reduction

Enhances tools for studying symmetries in algebraic geometry

Abstract

Let $X$ be a smooth scheme with an action of an algebraic group $G$. We establish an equivalence of two categories related to the corresponding moment map $\mu : T^*X \to Lie(G)^*$ - the derived category of G-equivariant coherent sheaves on the derived fiber $\mu^{-1}(0)$ and the derived category of $G$-equivariant matrix factorizations on $T^*X \times Lie(G)$ with potential given by $\mu$.