Deformations of vector bundles on coisotropic subvarieties via the Atiyah class

2010/10/18 by Pecharich, Jeremy
#14D15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1010.3671

Abstract

Using the Atiyah class we give a criterion for a vector bundle on a coisotropic subvariety, Y, of an algebraic Poisson variety X to admit a first and second order noncommutative deformation. We also show noncommutative deformations of a vector bundle are governed by a curved dg Lie algebra which reduces to the classical relative Hochschild complex when the Poisson structure on X is trivial.

Related

• Deformation of line bundles on coisotropic subvarieties
• Deformations of algebras in noncommutative geometry
• The geometric deformation of curved L_∞ algebras and Lie algebroids
• Gerstenhaber-Batalin-Vilkoviski structures on coisotropic intersections
• Chern classes of quantizable coisotropic bundles