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

TL;DR

This paper proves that certain regular projective surfaces over fields of characteristic at least 7 are geometrically integral when their anti-canonical divisors are nef.

Contribution

It establishes a new result linking nef anti-canonical divisors to geometric integrality over imperfect fields in characteristic at least 7.

Findings

Surfaces with nef anti-canonical divisors are geometrically integral over the base field.

The result applies to regular projective surfaces over fields with characteristic p ≥ 7.

The paper advances understanding of the geometry of surfaces in positive characteristic.

Abstract

We prove that a regular projective surface $S$ over a field $k$ of characteristic $p \ge 7$, with $H^0(S,\mathcal{O}_S) = k$ and $-K_S$ being nef, is geometrically integral over $k$.