Tue, February 18, 2014
3:00 pm - 4:00 pm
MW 154
Title: Stability and the McKay correspondence
Seminar Type: Algebraic Geometry
Speaker: Morgan Brown, University of Michigan
Abstract: Let G be a subgroup of SL_n(\C). When n=2, \C^n/G has a unique minimal resolution, and the classical McKay correspondence relates the representation theory of G with the structure of this resolution. For n=3, Bridgeland, King, and Reid used categorical techniques to show that \C^n/G$ has a distinguished crepant resolution Y=G-Hilb. Specifically, they showed that there is an equivalence between the derived categories D^G(\C^n) and D(Y). I will show how one can use a notion of stability to describe coherent sheaves on Y in terms of complexes of G-equivariant objects on \C^n.