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arXiv · 2004.05536

Vanishing for Hodge ideals of $\mathbb{Q}$-divisors

Bingyi Chen
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Abstract

Musta\c{t}\u{a} a and Popa introduce the notion of Hodge ideals for an effective $\mathbb{Q}$-divisor $D$ and prove a vanishing theorem for Hodge ideals, which generalizes Nadel vanishing for multiplier ideals. However, their proof needs an extra assumption on the existence of $\ell$-roots of the line bundle $\mathscr{O}_X(\ell D)$, which is not necessary for Nadel vanishing. In this paper, we prove that vanishing for Hodge ideals still holds even without this assumption.

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Bingyi Chen. 2020-04-12. Vanishing for Hodge ideals of $\mathbb{Q}$-divisors. https://arxiv.org/abs/2004.05536

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