VOL. 88 | 2023 An introduction to Hilbert schemes of points on ADE singularities
Alastair Craw

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 119-157 (2023) DOI: 10.2969/aspm/08810119

Abstract

This paper is based on a talk at the conference The McKay correspondence, mutation and related topics from July 2020. We provide an introduction to joint work of the author with Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői [CGGS21b] that constructs the reduced scheme underlying the Hilbert scheme of $n$ points on an ADE singularity as a Nakajima quiver variety for a particular stability parameter. After drawing a parallel with two well-known constructions of the Hilbert scheme of $n$ points in $\mathbb{A}^2$, we summarise results of the author and Gwyn Bellamy [BC20] before describing the main result by cornering a noncommutative algebra obtained from the preprojective algebra of the framed McKay graph.

Information

Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810119

Subjects:
Primary: 16G20
Secondary: 13A50 , 14C05 , 14E16 , 14E30

Keywords: cornering , Kleinian orbifold , preprojective algebra , quiver variety , Quot scheme

Rights: Copyright © 2023 Mathematical Society of Japan

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