Weak Akizuki-Nakano vanishing theorem for globally $F$-split 3-folds

Abstract

In this paper, we prove that a weak form of the Akizuki-Nakano vanishing theorem holds on globally $F$-split 3-folds. Making use of this vanishing theorem, we study deformations of globally $F$-split Fano 3-folds and the Kodaira vanishing theorem for thickenings of locally complete intersection globally $F$-regular 3-folds.