Deformations of vector bundles on coisotropic subvarieties via the Atiyah class

Details Deformations of vector bundles on coisotropic subvarieties via the Atiyah class Deformations of vector bundles on coisotropic subvarieties via the Atiyah class

2010-10-18

arxiv.org/abs/1010.3671v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

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.

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