Motivic integration, quotient singularities and the McKay correspondence

TL;DR

This paper explores motivic integration on quotient singularities, providing a new proof of the McKay correspondence and extending results to more general singular spaces.

Contribution

It offers a novel proof of the McKay correspondence and generalizes motivic integration results to arbitrary singular spaces.

Findings

New proof of McKay correspondence for quotient singularities

Extended motivic integration techniques to arbitrary singular spaces

Contributed to the understanding of singularity invariants

Abstract

The present work is devoted to the study of motivic integration on quotient singularities. We give a new proof of a form of the McKay correspondence previously proved by Batyrev. The paper contains also some general results on motivic integration on arbitrary singular spaces.