Uniqueness of Tangent Cone of Kahler Einstein Metrics on Singular Varieties with Crepant Singularities

2022/08/10 by Xin Fu, Fu, Xin · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2208.05196

Abstract

Let (X, L) be a polarized Calabi Yau variety (or canonical polarized variety) with crepant singularity. Suppose ω_KE ∈ c₁(L) (or ω_KE ∈ c₁(K_X)) is the unique Ricci flat current (or Kahler Einstein current with negative scalar curvature) with local bounded potential constructed in [18], we show that the local tangent at any point p ∈ X of metric ω_KE is unique

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