Quantization of line bundles on Lagrangian subvarieties

TL;DR

This paper establishes a precise criterion for when line bundles on smooth Lagrangian subvarieties can be deformed into modules over a deformation quantization of an algebraic symplectic variety, using formal geometry techniques.

Contribution

It provides a necessary and sufficient condition for deforming line bundles on Lagrangian subvarieties within the framework of deformation quantization, advancing understanding of quantization in algebraic geometry.

Findings

Derived a criterion for deformation of line bundles

Connected formal geometry with deformation quantization

Applied results to algebraic symplectic varieties

Abstract

We apply the technique of formal geometry to give a necessary and sufficient condition for a line bundle supported on a smooth Lagrangian subvariety to deform to a sheaf of modules over a fixed deformation quantization of the structure sheaf of an algebraic symplectic variety.