K-stability of del Pezzo surfaces with a single quotient singularity

TL;DR

This paper investigates the K-stability of certain del Pezzo surfaces with a single quotient singularity, focusing on cases where the minimal resolution has exactly two exceptional curves with specified self-intersection numbers.

Contribution

It provides a detailed analysis of the K-stability conditions for del Pezzo surfaces with specific singularities and minimal resolutions.

Findings

Characterization of K-stability for these surfaces

Conditions on the exceptional curves for stability

Extension of stability criteria to singular del Pezzo surfaces

Abstract

In this paper, we study the K-stability of del Pezzo surfaces with a single quotient singularity whose minimal resolution admits exactly two exceptional curves \(E_1\) and \(E_2\) with \(E_{1}^2=-n\), \(E_{2}^2=-m\) for \(n,m\geq 2\).