A vanishing theorem for threefolds in characteristic $p>5$ and applications

TL;DR

This paper proves a Kawamata-Viehweg vanishing theorem for threefolds in characteristic p>5 and applies it to derive results on the structure and singularities of klt threefolds and Mori fiber spaces.

Contribution

It establishes a new vanishing theorem in positive characteristic and applies it to key problems in the geometry of threefolds.

Findings

Vanishing of higher direct images for Mori fiber spaces

Validation of Kollár's local vanishing in characteristic p>5

Rationality of singularities of the base of a conic bundle

Abstract

In this note we show a Kawamata-Viehweg vanishing theorem for pl-contractions on threefolds in characteristic $p>5$. We deduce several applications for klt threefolds: the vanishing of higher direct images of structure sheaves of Mori fibre spaces, Koll\'ar's result on local vanishing and the rationality of the singularities of the base of a conic bundle.