Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic

Abstract

We show that the Bogomolov-Sommese vanishing theorem holds for a log canonical projective surface in large characteristic unless the Iitaka dimension of the round-down of the log canonical divisor is not equal to two. As an application, we prove that a log resolution of a pair of a normal projective surface and a reduced divisor in large characteristic lifts to the ring of Witt vectors when the Iitaka dimension of the log canonical divisor is less than or equal to zero. Moreover, we give explicit and optimal bounds on the characteristic unless their Iitaka dimensions are equal to zero.

arXiv comment29 pages, final version, to appear in Advances in Mathematics

References in corpus (8)

• Differential Forms on Log Canonical Spaces
• Globally $F$-regular and log Fano varieties
• Smoothable del Pezzo surfaces with quotient singularities
• Simply connected surfaces of general type in positive characteristic via deformation theory
• Families over special base manifolds and a conjecture of Campana
• The maximal number of singular points on log del Pezzo surfaces
• Differential forms on log canonical spaces in positive characteristic
• Birational geometry of compactifications of Drinfeld half-spaces over a finite field