Surfaces of globally $F$-regular and $F$-split type

TL;DR

This paper proves that certain algebraic surfaces with dense globally F-split or F-regular properties are classified as Calabi-Yau or Fano types, respectively, contributing to the understanding of their geometric structure.

Contribution

It establishes a classification result linking globally F-split and F-regular surfaces to Calabi-Yau and Fano types, respectively, in algebraic geometry.

Findings

Surfaces of dense globally F-split type are Calabi-Yau type.

Surfaces of dense globally F-regular type are Fano type.

Provides a classification framework for these surfaces.

Abstract

We prove that normal projective surfaces of dense globally $F$-split type (resp. globally $F$-regular type) are of Calabi-Yau type (resp. Fano type).