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arXiv · 2604.13823

Mumford vanishing for threefolds in positive characteristic

Tatsuro Kawakami·Hiromu Tanaka
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Abstract

Let $X$ be a projective klt threefold in characteristic $p>5$ and let $L$ be a nef Cartier divisor on $X$. We show that $H^1(X, -L)=0$ for the following two cases: (1) $K_X$ is not big and $L$ is big; (2) $-K_X$ is nef and $L$ is of numerical dimension two.

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Tatsuro Kawakami, Hiromu Tanaka. 2026-04-15. Mumford vanishing for threefolds in positive characteristic. https://arxiv.org/abs/2604.13823

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