McKay correspondence for isolated Gorenstein singularities

Abstract: The McKay correspondence is a (natural) correspondence between the (non-trivial) irreducible representations of a finite subgroup G of SL(2,C) and the irreducible components of the exceptional divisor of a minimal resolution of the associated quotient singularity C^2//G. A geometric construction for this correspondence was given by González-Sprinberg and Verdier, who showed that the two sets also correspond bijectively to the set of indecomposable reflexive modules on the quotient singularity. This was generalised to higher dimensional quotient singularities (i.e., quotient of C^n by a finite subgroup of SL(n,C)) by Ito-Reid, where the above sets were substituted by certain smaller subsets. It was further generalised to more general quotient singularities by Bridgeland-King-Reid, Iyama-Wemyss and others, using the language of derived categories. In this talk, I will survey past results and discuss what happens for the isolated Gorenstein singularities case (not necessarily a quotient singularity). If time permits, I will discuss applications to Matrix factorization. This is joint work in progress with J. F. de Bobadilla and A. Romano-Velazquez.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html