paper

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

arXiv:2208.05196

Abstract

Let $(X, L)$ be a polarized Calabi Yau variety (or canonical polarized variety) with crepant singularity. Suppose $I ¨ _{K E} \in c_{1} (L)$ (or $I ¨ _{K E} \in c_{1} (K_{X})$ ) 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 $p \in X$ of metric $I ¨ _{K E}$ is unique

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