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

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