Deformation of line bundles on coisotropic subvarieties

TL;DR

This paper establishes a criterion for when line bundles on smooth coisotropic subvarieties can be deformed into quantized versions within algebraic Poisson structures.

Contribution

It introduces a specific criterion for the first order deformation quantization of line bundles on coisotropic subvarieties.

Findings

Provides a necessary and sufficient condition for deformation quantization.

Connects geometric properties of coisotropic subvarieties with algebraic quantization.

Advances understanding of deformation theory in Poisson geometry.

Abstract

We prove a criterion stating when a line bundle on a smooth coisotropic subvariety Y of a smooth variety X with an algebraic Poisson structure, admits a first order deformation quantization.