Classification of log del Pezzo surfaces of index three

TL;DR

This paper classifies all log del Pezzo surfaces of index three, a specific class of algebraic surfaces with particular divisor properties, using Nakayama's classification techniques.

Contribution

It provides a complete classification of log del Pezzo surfaces of index three, expanding understanding of their structure and properties.

Findings

Complete list of log del Pezzo surfaces of index three

Identification of key geometric properties

Application of Nakayama's classification method

Abstract

A normal projective non-Gorenstein log-terminal surface $S$ is called a log del Pezzo surface of index three if the three-times of the anti-canonical divisor $-3K_S$ is an ample Cartier divisor. We classify all of the log del Pezzo surfaces of index three. The technique for the classification based on the argument of Nakayama.