Mumford vanishing for threefolds in positive characteristic

Tatsuro Kawakami; Hiromu Tanaka

Mumford vanishing for threefolds in positive characteristic

Algebraic Geometry 2026-04-16 v1

Authors: Tatsuro Kawakami , Hiromu Tanaka

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.

Keywords

Mumford vanishing positive characteristic klt threefolds nef divisors cohomology

Cite

@article{arxiv.2604.13823,
  title  = {Mumford vanishing for threefolds in positive characteristic},
  author = {Tatsuro Kawakami and Hiromu Tanaka},
  journal= {arXiv preprint arXiv:2604.13823},
  year   = {2026}
}

Comments

18 pages

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