A note on orbifold regularity of canonical metrics

2025/09/11 by Guenancia, Henri, Pan, Chung-Ming, Păun, Mihai
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.09259

Abstract

In this short note, we prove that on a compact Kähler variety X with log terminal singularities and c₁(X)=0, any singular Ricci-flat Kähler metric has orbifold singularities in restriction to the orbifold locus of X.

Citations

• Kähler families of Green's functions
• Orbifold modifications of complex analytic varieties
• Strict positivity of Kähler-Einstein currents
• Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
• Diameter estimates in Kähler geometry
• Algebraic approximation and the decomposition theorem for Kähler Calabi-Yau varieties
• On Yau's theorem for effective orbifolds
• Calabi-Yau manifolds with isolated conical singularities
• Orbifold regularity of weak Kahler-Einstein metrics
• Singular Kahler-Einstein metrics
• Orbifoldes à premi\ere classe de Chern nulle

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• Orbifold regularity of weak Kahler-Einstein metrics
• Remarks on Singular Kähler-Einstein Metrics
• Variation of singular Kähler-Einstein metrics: Kodaira dimension zero
• Constant Scalar Curvature Kähler Metrics on Resolutions of an Orbifold Singularity of Depth 1
• Existence of complete Kahler Ricci-flat metrics on crepant resolutions