Equivariant resolution of singularities in characteristic 0

TL;DR

This paper presents a new proof for resolving singularities in algebraic geometry when a finite group acts on the variety, assuming known resolutions without group actions, and reduces the general case to toroidal singularities.

Contribution

It introduces a novel proof technique for equivariant resolution of singularities in characteristic zero, leveraging reduction to toroidal cases.

Findings

Established equivariant resolution for toroidal singularities.

Reduced general equivariant resolution to the toroidal case.

Provided a new proof framework assuming existing non-equivariant resolutions.

Abstract

A new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided. We assume we know how to resolve singularities without group action. We first prove equivariant resolution of toroidal singularities. Then we reduce the general case to the toroidal case.