#### Vol. 14, No. 2, 2020

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Singularity categories of deformations of Kleinian singularities

### Simon Crawford

Vol. 14 (2020), No. 2, 349–382
##### Abstract

Let $G$ be a finite subgroup of $SL\left(2,k\right)$ and let $R=k{\left[x,y\right]}^{G}$ be the coordinate ring of the corresponding Kleinian singularity. In 1998, Crawley-Boevey and Holland defined deformations ${\mathsc{𝒪}}^{\lambda }$ of $R$ parametrised by weights $\lambda$. In this paper, we determine the singularity categories ${\mathsc{𝒟}}_{sg}\left({\mathsc{𝒪}}^{\lambda }\right)$ of these deformations, and show that they correspond to subgraphs of the Dynkin graph associated to $R$. This generalises known results on the structure of ${\mathsc{𝒟}}_{sg}\left(R\right)$. We also provide a generalisation of the intersection theory appearing in the geometric McKay correspondence to a noncommutative setting.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 3.236.212.116 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.