Kawamata-Viehweg Vanishing on Rational Surfaces in Positive Characteristic

TL;DR

This paper proves the Kawamata-Viehweg vanishing theorem for rational surfaces in positive characteristic by leveraging lifting properties, extending its validity to log del Pezzo surfaces.

Contribution

It establishes the Kawamata-Viehweg vanishing theorem on rational surfaces in positive characteristic using lifting techniques, a significant extension of known results.

Findings

Vanishing theorem holds on rational surfaces in positive characteristic

Extension to log del Pezzo surfaces

Lifting property to W_2(k) is key

Abstract

We prove that the Kawamata-Viehweg vanishing theorem holds on rational surfaces in positive characteristic by means of the lifting property to W_2(k) of certain log pairs on smooth rational surfaces. As a corollary, the Kawamata-Viehweg vanishing theorem holds on log del Pezzo surfaces in positive characteristic.