Uniqueness of tangent cone of Kähler-Einstein metrics on singular varieties with crepant singularities

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作者：
Xin Fu
机构：
[1] University of California,Department of Mathematics
来源：
Mathematische Annalen | 2024年 / 388卷
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摘要：
Let (X, L) be a polarized Calabi-Yau variety (or canonical polarized variety) with crepant singularities. Suppose ωKE∈c1(L)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _{KE}\in c_1(L)$$\end{document} (or ωKE∈c1(KX))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _{KE}\in c_1(K_X))$$\end{document} is the unique Ricci flat current (or Käher-Einstein current with negative scalar curvature) with local bounded potential constructed in (Eyssidieux in J Am Math Soc 22: 607-639, 2009), we show that the local tangent at any point p∈X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\in X$$\end{document} of metric ωKE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _{KE}$$\end{document} is unique.
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页码：3229 / 3258
页数：29
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