Kahler-Einstein metric near an isolated log canonical singularity

2021/06/10 by Ved Datar, Datar, Ved, Xin Fu +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDE #Analysis of PDEs (math.AP) #Differential Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2106.05486

openalex publication_date 2021/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Kahler-Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable. In complex dimension 2, we show that any complete Kahler-Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to one of the model metrics constructed by Kobayashi and Nakamura arising from hyperbolic geometry.

Citations

• Differential equations on riemannian manifolds and their geometric applications

Cited by

• On multiscale aspects of Kähler-Einstein metrics and algebraic geometry

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