Classifying log del Pezzo surfaces with torus action

TL;DR

This paper classifies log del Pezzo surfaces with torus actions based on their singularity properties, providing explicit classifications for specific cases of Gorenstein index using a new algorithm.

Contribution

It introduces a concrete classification algorithm for log del Pezzo surfaces with torus actions for fixed k, including explicit results for k=1, 2, and 3.

Findings

Explicit classification for k=1, 2, 3

Algorithm for classifying these surfaces

Results for Gorenstein index 1, 2, 3

Abstract

We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/k-log canonical if it allows a resolution of singularities with discrepanies all greater or equal to 1/k-1. We provide a concrete classification algorithm for fixed k and give explicit results for k=1, 2 and 3. This comprises in particular the cases of Gorenstein index 1, 2 and 3.