Algebraic Geometry Seminar
Derived Reid'S Recipe for Abelian Subgroups of Sl3(C)
Speaker: Timothy Logvinenko, Cardiff University
Location: Warren Weaver Hall 317
Date: Tuesday, October 29, 2013, 3:30 p.m.
Synopsis:
The classical McKay correspondence is a 1-1 correspondence between non-trivial irreducible representations of a finite subgroup G of SL2(C) and irreducible divisors on the minimal resolution Y of C2/G. In this talk I describe joint work with Sabin Cautis and Alastair Craw in which we generalize this correspondence to dimension three using the famous Bridgeland-King-Reid derived equivalence. Specifically, we show that one can naturally extract from this equivalence a correspondence between irreducible representations of subrgroups G of SL3(C) and exceptional subvarieties of Y = G-Hilb(C3). The same method applied to subgroups G of SL2(C) produces the classical McKay.