Quantization of vector bundles on Lagrangian subvarieties

2017/01/06 by Baranovsky, Vladimir, Chen, Taiji
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.01542

Abstract

We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure sheaf of X, we establish when E admits a deformation quantization to a module over Oh. If the necessary conditions hold, we describe the set of equivalence classes of such quantizations.

Related

• Quantization of line bundles on Lagrangian subvarieties
• Chern classes of quantizable coisotropic bundles
• Deformation quantization and perverse sheaves
• A new construction of strict deformation quantization for Lagrangian fiber bundles
• Deformation Quantization in Algebraic Geometry