Geometric singularities of regular surfaces with nef anti-canonical divisors over imperfect fields

Chongning Wang; Lei Zhang

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arXiv · 2604.05293

Geometric singularities of regular surfaces with nef anti-canonical divisors over imperfect fields

Chongning Wang·Lei Zhang

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Abstract

Let $S$ be a regular projective surface over a field $k$ of characteristic $p>0$, with $H^0(S,\mathcal{O}_S)=k$ and $-K_S$ nef. We prove that $S$ is geometrically integral over $k$ when $p\geq 7$, and we also find an example of $S$ that is not geometrically integral when $p=5$.

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Chongning Wang, Lei Zhang. 2026-04-07. Geometric singularities of regular surfaces with nef anti-canonical divisors over imperfect fields. https://arxiv.org/abs/2604.05293

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