Classification of globally F-regular $F$-sandwiches of Hirzebruch surfaces

TL;DR

This paper classifies globally F-regular F-sandwiches of Hirzebruch surfaces, providing a detailed understanding of their structure in positive characteristic algebraic geometry.

Contribution

It offers the first classification of globally F-regular F-sandwiches specifically for Hirzebruch surfaces, expanding knowledge of Frobenius splittings.

Findings

Complete classification of globally F-regular F-sandwiches of Hirzebruch surfaces

Identification of structural properties of these F-sandwiches

Insights into Frobenius splitting behavior in positive characteristic

Abstract

Let $X$ be a smooth variety over an algebraically closed field of positive characteristic. An $F$-sandwich of $X$ is a normal variety $Y$ through which the relative Frobenius morphism of $X$ factors as $F:X\rightarrow Y \rightarrow X$. In this paper, we give a classification of globally F-regular $F$-sandwiches of Hirzebruch surfaces.