Extension of adapted differentials on klt orbifolds

TL;DR

This paper proves that for klt orbifolds, adapted reflexive differentials can be extended to regular differentials on a resolution, advancing the understanding of differential forms on singular orbifolds.

Contribution

It establishes the extension property of adapted reflexive differentials on klt orbifolds, a new result in the study of differential forms on singular spaces.

Findings

Reflexive differentials extend to resolutions in klt orbifolds.

Extension holds on suitably ramified covers.

Advances the theory of differential forms on singular orbifolds.

Abstract

Given a geometric orbifold $(X,\Delta)$ in the sense of Campana, adapted reflexive differentials with respect to this orbifold are defined on suitably ramified covers of $X$. We show that if the orbifold $(X,\Delta)$ is klt, then any such reflexive differential form can be extended to a regular differential form on a resolution of singularities of the cover.