Counting resolutions of symplectic quotient singularities
Gwyn Bellamy (Glasgow)
Monday 19th January, 2015 16:00-17:00 Maths 204
If V is a symplectic vector space and G a finite subgroup of Sp(V), then the quotient singularity V/G is a very interesting object to study, both from the geometric and representation-theoretic point of view. One of the motivational problems in trying to understand the singularities of V/G is that of deciding whether V/G admits a symplectic resolution or not. More generally, one can ask how many symplectic resolutions it admits. The goal of this talk is to explain how one can count the number of symplectic resolutions of V/G. I'll present an explicit formula for this number in terms of the dimension of a certain Orlik-Solomon algebra. The key to deriving this formula is to relate the resolutions of V/G to the Calogero-Moser deformations, where one can use the representation theory of symplectic reflection algebras.