Log del Pezzo surfaces with not small fractional indices

TL;DR

This paper classifies log del Pezzo surfaces with fractional indices at least 1/2, extending the understanding of their structure using Nakayama's technique.

Contribution

It provides a complete classification of log del Pezzo surfaces with fractional index ≥ 1/2, a previously unresolved problem in algebraic geometry.

Findings

Classified all log del Pezzo surfaces with r(S) ≥ 1/2

Extended Nakayama's technique to this classification

Identified new structural properties of these surfaces

Abstract

For a log del Pezzo surface $S$, the fractional index $r(S)\in\mathbb{Q}_{>0}$ is the maximum of $r$ with which $-K_S$ can be written as $r$ times some Cartier divisor. We classify all the log del Pezzo surfaces $S$ with $r(S)\geq 1/2$, after the technique of Nakayama.