A homological approach to singular reduction in deformation quantization

TL;DR

This paper introduces a homological method for deformation quantization of singular symplectic quotients, especially where the moment map's coefficients form a complete intersection, handling complex singularities beyond orbifolds.

Contribution

It develops a homological quantum reduction technique for singular symplectic quotients with complete intersection conditions, expanding quantization methods to more complex singularities.

Findings

Constructed deformation quantization on singular quotients

Applied to examples with complex singularities

Extended quantization to non-orbifold singularities

Abstract

We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are discussed, among others one where the singularity type is worse than an orbifold singularity.