On Saito's vanishing theorem

TL;DR

This paper provides a new proof of Saito's vanishing theorem for mixed Hodge modules using a method involving branched coverings, emphasizing the strictness of direct images.

Contribution

It introduces a novel proof technique for Saito's vanishing theorem based on the strictness of direct images on branched coverings.

Findings

Reproves Saito's vanishing theorem using a different method.

Highlights the role of strictness of direct images in the proof.

Connects the proof technique to branched coverings.

Abstract

We reprove Saito's vanishing theorem for mixed Hodge modules by the method of Esnault and Viehweg. The main idea is to exploit the strictness of direct images on certain branched coverings.