# Søren Gammelgaard: Quiver varieties and moduli spaces attached to Kleinian singularities

**Time: **
Fri 2022-04-01 13.15 - 14.15

**Location: **
Zoom, meeting ID: 698 8663 6380

**Participating: **
Søren Gammelgaard (University of Oxford)

### Abstract

We discuss how Nakajima's quiver varieties can be used to understand the Hilbert schemes of points on Kleinian singularities, that is, singular surfaces isomorphic to \(\mathbb{C}^2/G\), for *G* a finite subgroup of \(\mathrm{SL}_2(\mathbb{C})\).

This approach lets us show that each such Hilbert scheme is irreducible, has symplectic singularities, and has a unique symplectic resolution.

Time permitting, we may touch upon a type of “equivariant Quot scheme” associated to the same singularity, or possibly a generalisation to sheaves on a stacky “compactification” of the same singular surface.

This is joint work with A. Craw, Á. Gyenge, and B. Szendrői.