Adam Gyenge (Oxford)

Title: Hilbert and Quot schemes of simple surface singularities

Abstract: The Hilbert schemes of points on the affine complex plane
has the structure of a Nakajima quiver variety. For a finite subgroup
G of SL(2, C), I will discuss the construction of the Hilbert scheme
of n points on the Kleinian singularity C^2/G as a Nakajima quiver
variety for the framed McKay quiver of G with a specific non-generic
stability parameter. I will also present a formula for the generating
series collecting the Euler numbers of these varieties, a specific
case of which was proved recently by Nakajima. Given enough time, I
will explain the analogous problem for certain Quot schemes of C^2/G.
(Joint work with Alastair Craw, Soren Gammelgaard and Balazs
Szendroi).