Klt del Pezzo surfaces which are not globally F-split

TL;DR

This paper constructs a specific type of algebraic surface, a klt del Pezzo surface, that does not exhibit the globally F-split property in positive characteristic fields.

Contribution

It provides the first explicit example of a klt del Pezzo surface lacking the globally F-split property in positive characteristic.

Findings

Constructed a klt del Pezzo surface not globally F-split

Demonstrated existence over any algebraically closed field of positive characteristic

Advances understanding of F-singularity properties in algebraic geometry

Abstract

We construct a klt del Pezzo surface which is not globally F-split, over any algebraically closed field of positive characteristic.