Extension Theorems for differential forms on low-dimensional good quotients

TL;DR

This paper proves that differential forms on certain low-dimensional quotient spaces can be pulled back to resolutions without losing regularity, extending understanding of differential forms in quotient geometry.

Contribution

It establishes extension theorems for differential forms on low-dimensional good quotients, a new result in the study of quotient singularities.

Findings

Pull-back of differential forms remains regular on resolutions in dimension three and four.

Extension theorems hold for differential forms on good quotients of low dimension.

Provides new tools for studying differential forms on quotient singularities.

Abstract

In this paper we will show that the pull-back of any regular differential form defined on the smooth locus of a good quotient of dimension three and four to any resolution yields a regular differential form.