Characterization of log del Pezzo pairs via anticanonical models

TL;DR

This paper characterizes smooth log del Pezzo pairs through anticanonical models, classifies certain non-rational pairs, and links globally F-regular surfaces to Fano type, advancing understanding of algebraic surface classifications.

Contribution

It introduces a unified definition of log del Pezzo pairs, characterizes smooth cases via anticanonical models, and establishes new classifications and properties of algebraic surfaces.

Findings

Smooth log del Pezzo pairs characterized by anticanonical models

Classification of non-rational weak log canonical del Pezzo pairs

Every globally F-regular surface is of Fano type

Abstract

There are several variations of the definition of log del Pezzo pairs in the literature. We define their suitable smooth models, and we show that they are the same. In particular, we obtain a characterization of smooth log del Pezzo pairs in terms of anticanonical models. As applications, we classify non-rational weak log canonical del Pezzo pairs, and we prove that every surface of globally F-regular type is of Fano type.