Extension theorems for differential forms and Bogomolov-Sommese vanishing on log canonical varieties

TL;DR

This paper proves extension theorems for differential forms on log canonical varieties, showing that reflexive differentials can be extended with poles and generalizing the Bogomolov-Sommese vanishing theorem to threefolds.

Contribution

It establishes extension results for differential forms on log canonical varieties and generalizes the Bogomolov-Sommese vanishing theorem to threefold pairs.

Findings

Extension of p-forms with logarithmic poles on log canonical pairs.

Reflexive differentials have good pull-back properties.

Generalization of Bogomolov-Sommese vanishing to threefolds.

Abstract

Given a p-form defined on the smooth locus of a normal variety, and a resolution of singularities, we study the problem of extending the pull-back of the p-form over the exceptional set of the desingularization. For log canonical pairs and for certain values of p, we show that an extension always exists, possibly with logarithmic poles along the exceptional set. As a corollary, it is shown that sheaves of reflexive differentials enjoy good pull-back properties. A natural generalization of the well-known Bogomolov-Sommese vanishing theorem to log canonical threefold pairs follows.