Vanishing for Hodge ideals on toric varieties

TL;DR

This paper develops a Koszul-type resolution for differential forms on smooth toric varieties and proves a vanishing theorem for Hodge ideals linked to effective ivisors, extending prior results in the field.

Contribution

It introduces a new resolution method and establishes a Nadel-type vanishing theorem for Hodge ideals on smooth projective toric varieties, broadening existing theoretical frameworks.

Findings

Constructed a Koszul-type resolution for sheaves of differential forms.

Proved a Nadel-type vanishing theorem for Hodge ideals.

Extended earlier results of Must and Popa.

Abstract

In this article we construct a Koszul-type resolution of the p-th exterior power of the sheaf of holomorphic differential forms on smooth toric varieties and use this to prove a Nadel-type vanishing theorem for Hodge ideals associated to effective \mathbb{Q}-divisors on smooth projective toric varieties. This extends earlier results of Musta\c{t}\u{a} and Popa.