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).

algebraic geometry

Audience: researchers in the topic

Warwick algebraic geometry seminar