DMM Seminar

Speaker: Daniel Halpern-Leistner (UC Berkeley)
Title: The derived category of a GIT quotient
Date (JST): Mon, Jul 02, 2012, 13:00 - 17:00
Place: Seminar Room B
Abstract: For a variety X acted on by a reductive group, one can consider the derived category of equivariant coherent sheaves on X, or the derived category of a GIT quotient of X. In this talk I will describe a relationship between these two categories: among other things the category of the GIT quotient can be embedded as a full subcategory of the equivariant category. This is a generalization of a description of B-type D-branes in geometric phases of gauged linear sigma models obtained by Hori, Herbst, and Page.

In the first part of the talk, I will describe the main theorem for smooth X and explain how it is a common generalization of several classical results: Serre's description of the category of modules on a projective variety, localization and surjectivity theorems for the equivariant cohomology of a variety with a Hamiltonian group action, and the 'quantization commutes with reduction' theorem. In the second half of the talk, I will present some applications of the theory: constructing new examples of derived equivalences between birational varieties, and constructing new derived autoequivalences for certain GIT quotients. I will also discuss extensions of the main theorem to singular X and connections with the work of Cautis et al. on stratified Mukai flops.
Remarks: Break 14:00-15:30