Vanishing Theorem for Hodge Ideals on smooth hypersurfaces

TL;DR

This paper proves a vanishing theorem for Hodge ideals on smooth hypersurfaces using a Koszul-type resolution, extending previous results and contributing to the understanding of Hodge theory in algebraic geometry.

Contribution

It introduces a new vanishing theorem for Hodge ideals on hypersurfaces, generalizing earlier work by Mustata and Popa with a novel proof technique.

Findings

Established a weak Bott's vanishing theorem for hypersurfaces

Proved a vanishing theorem for Hodge ideals on hypersurfaces

Extended previous results to a broader class of divisors

Abstract

We use a Koszul-type resolution to prove a weak version of Bott's vanishing theorem for smooth hypersurfaces in $\mathbb{P}^n$ and use this result to prove a vanishing theorem for Hodge ideals associated with an effective Cartier divisor on a hypersurface. This extends an earlier result of Mustata and Popa.