Intermediate complex structure limit for Calabi-Yau metrics

• 成果类型: Article
• 署名作者: Li, Yang
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01314-9
• 发表日期: 2025
• 页码: 459-496
• 关键词: kahler-manifolds

摘要

We study polarised degenerations of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n$\end{document}-dimensional Calabi-Yau hypersurfaces {F0F1 & mldr;Fm+tF=0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{ F_{0}F_{1}\ldots F_{m}+tF=0\} $\end{document}, where the essential skeleton has dimension 1 <= m <= n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1\leq m\leq n-1$\end{document}. We will describe the limiting behaviour of the Calabi-Yau potential at the C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C<^>{0}$\end{document}-level, in terms of an optimal transport problem, and in terms of non-archimedean potential theory.