Tony Pantev : Quantization of Fourier-Mukai transforms

Posted by , part of the Algebraic Geometry Seminar.

At

Feb. 9, 2011, 4 p.m.

In

SEO 1227

Abstract

I will discuss the deformation theory of Fourier-Mukai transforms in a general complex analytic setting. Suppose that X and Y are two complex manifolds and P is a coherent sheaf on the product which implements an equivalence between the coherent derived categories of X and Y. Given an arbitrary formal quantization of X we construct a unique quantization of Y such that the Fourier-Mukai transform deforms to an equivalence of the derived categories of the quantizations. Here quantizations are understood in the framework of stacks of algebroids. This is a joint work with D.Arinkin and J.Block.