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.

arXiv comment29 pages; v2: minor changes

References in corpus (8)

• Globally $F$-regular and log Fano varieties
• The canonical sheaf of Du Bois singularities
• Grothendieck Duality for Deligne-Mumford Stacks
• The deformation theory of local complete intersections
• Simply connected surfaces of general type in positive characteristic via deformation theory
• The Minimal Model Program for threefolds in characteristic five
• Differential forms on log canonical spaces in positive characteristic
• Bogomolov--Sommese type vanishing for globally $F$-regular threefolds

Cited by in corpus (1)

• On asymptotic socle degrees of local cohomology modules