Semi-negativity of Hodge bundles associated to Du Bois families

TL;DR

This paper proves that for a family of Du Bois schemes, the associated sheaf $R^1 f_* \

Contribution

It establishes the semi-negativity (anti-nef property) of the sheaf $R^1 f_* \\mathcal{O}_X$ in the context of Du Bois families, a new result in algebraic geometry.

Findings

The sheaf $R^1 f_* \\mathcal{O}_X$ is anti-nef.

The dual of this sheaf is nef.

The result applies to families of Du Bois schemes of pure dimension.

Abstract

In this note we show that the sheaf $R^1 f_* \mathcal{O}_X$ is an anti-nef vector bundle (i.e., its dual is nef), where $f : X \to Y$ is a family of Du Bois schemes of pure dimension.