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

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.