McKay correspondence and orbifold equivalence

TL;DR

This paper establishes a connection between singularities related by the McKay correspondence and demonstrates their orbifold equivalence, providing a new proof for McKay type equivalence in matrix factorization categories.

Contribution

It introduces a novel proof linking McKay correspondence transformations to orbifold equivalence, extending understanding of singularity relationships.

Findings

Singularities related by McKay correspondence are orbifold equivalent.

New proof of McKay type equivalence for matrix factorization categories.

Establishes a theoretical link between singularity transformations and orbifold theory.

Abstract

We prove that a pair of singularities related by a transformation arising from the McKay correspondence are orbifold equivalent. From this we deduce a new proof of a McKay type equivalence for the matrix factorization categories.