On log del Pezzo surfaces in large characteristic

TL;DR

This paper investigates log del Pezzo surfaces over algebraically closed fields of large characteristic, establishing conditions for global F-regularity or liftability, and proving the Kawamata-Viehweg vanishing theorem in this setting.

Contribution

It demonstrates that klt del Pezzo surfaces in large characteristic are either globally F-regular or liftable, and proves Kawamata-Viehweg vanishing in this context.

Findings

Klt del Pezzo surfaces are globally F-regular or liftable in large characteristic.

Kawamata-Viehweg vanishing theorem holds for klt del Pezzo surfaces in large characteristic.

Provides conditions linking surface singularities and characteristic for algebraic geometry applications.

Abstract

We show that any Kawamata log terminal del Pezzo surface over an algebraically closed field of large characteristic is globally F-regular or it admits a log resolution which is liftable to characteristic zero. As a consequence, we prove the Kawamata-Viehweg vanishing theorem for klt del Pezzo surfaces of large characteristic.