Chern classes of quantizable coisotropic bundles

2021/04/01 by Baranovsky, Vladimir
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2104.00810

Abstract

Let M be a smooth algebraic variety of dimension 2(p+q) with an algebraic symplectic form and a compatible deformation quantization O_h of the structure sheaf. Consider a smooth coisotropic subvariety j: Y → M of codimension q and a vector bundle E on Y. We show that if j_* E admits a deformation quantization (as a module) then its characteristic class \widehatA(M) exp(-c(O_h)) ch(j_* E) lifts to a cohomology group associated to the null foliation of Y. Moreover, it can only be nonzero in degrees 2q, …, 2(p+q). For Lagrangian Y this reduces to a single degree 2q. Similar results hold in the holomorphic category. This is a companion paper of a joint work with Victor Ginzburg on general quantizable sheaves.

Related

• Quantization of vector bundles on Lagrangian subvarieties
• Quantization of line bundles on Lagrangian subvarieties
• Deformation Quantization in Algebraic Geometry
• Deformation of line bundles on coisotropic subvarieties
• Deformation quantization and perverse sheaves