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

2025/07/18 by In‐Kyun Kim, Kim, In-Kyun, Dae-Won Lee +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2507.13649

openalex publication_date 2025/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \(E₁\) and \(E₂\) with \(E₁²=-n\), \(E₂²=-m\) for \(n,m≥ 2\).

Citations

• On minimal model program and Zariski decomposition of potential triples
• δ-invariants of Du Val del Pezzo surfaces of degree 1
• δ-invariants of Du Val del Pezzo surfaces of degree 2
• δ-invariants of Du Val del Pezzo surfaces of degree 3
• K-stability of Fano varieties via admissible flags
• Uniqueness of K-polystable degenerations of Fano varieties
• Delta invariants of smooth cubic surfaces
• Del Pezzo surfaces with a single 1/k(1,1) singularity
• Thresholds, valuations, and K-stability
• Potentially non-klt locus and its applications
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• K-stability and Kähler-Einstein metrics
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• Log canonical thresholds of del Pezzo surfaces

Cited by

• Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero

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• Cylinders in del Pezzo surfaces with du Val singularities
• A 1-dimensional component of K-moduli of del Pezzo surfaces