On rank one log del Pezzo surfaces in characteristic different from two and three

TL;DR

This paper classifies rank one log del Pezzo surfaces over algebraically closed fields with characteristic not 2 or 3, and explores their properties and liftability to characteristic zero.

Contribution

It provides a complete classification of such surfaces and investigates their resolution and lifting properties in higher characteristics.

Findings

Classification of all rank one log del Pezzo surfaces in specified characteristics

Existence of log resolutions that lift to characteristic zero for characteristic > 5

Implications for the structure and properties of these surfaces

Abstract

We classify all log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic different from two and three. We also discuss some consequences of the classification. For example, we show that log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic higher than five admit a log resolution that lifts to characteristic zero over a smooth base.