Surfaces of globally $F$-regular type are of Fano type

TL;DR

This paper proves that projective surfaces with globally $F$-regular type over characteristic zero fields are of Fano type, linking positive characteristic properties to geometric classification in characteristic zero.

Contribution

It establishes a new connection between globally $F$-regular surfaces and Fano type surfaces in characteristic zero, expanding understanding of their geometric properties.

Findings

Globally $F$-regular type surfaces are of Fano type in characteristic zero.

The result bridges positive characteristic techniques with complex algebraic geometry.

Provides a classification link for algebraic surfaces based on $F$-regularity.

Abstract

We prove that a projective surface of globally $F$-regular type defined over a field of characteristic zero is of Fano type.