Dec 18 – 22, 2023
Kavli IPMU, Kashiwa, Japan
Asia/Tokyo timezone

Hilbert schemes and the Le Bruyn-Procesi theorem

Dec 18, 2023, 3:30 PM
50m
Lecture Hall (Kavli IPMU, Kashiwa, Japan)

Lecture Hall

Kavli IPMU, Kashiwa, Japan

Kashiwa, Japan

Speaker

Alastair Craw (Bath)

Description

For a positive integer n and a finite subgroup \Gamma in SL(2,C), I’ll describe work in preparation with Ryo Yamagishi which shows that the Hilbert scheme of n-points on C^2/\Gamma is reduced. In fact, it’s isomorphic to a Nakajima quiver variety, so it has symplectic singularities and it admits a unique crepant resolution. This strengthens previous joint work of mine with Gammelgaard, Gyenge and Szendroi. The main tool is a generalisation of the Le Bruyn-Procesi theorem which describes the invariant algebra for the natural action of the product of general linear groups on the space of representations of a quiver for a given dimension vector.

Presentation materials

There are no materials yet.