Classification of non-$F$-split del Pezzo surfaces of degree $1$

TL;DR

This paper classifies non-$F$-split del Pezzo surfaces of degree 1 using Fedder's criterion, providing a clear criterion for $F$-splitting based on their anti-canonical system.

Contribution

It offers a complete classification of non-$F$-split del Pezzo surfaces of degree 1 and establishes a criterion for $F$-splitting in terms of the anti-canonical system.

Findings

Classification of all non-$F$-split del Pezzo surfaces of degree 1

Necessary and sufficient criterion for $F$-splitting

Criterion expressed via anti-canonical system

Abstract

Using Fedder's criterion, we classify all non-$F$-split del Pezzo surfaces of degree $1$. We give a necessary and sufficient criterion for the $F$-splitting of such del Pezzo surfaces in terms of their anti-canonical system.