Intermediate complex structure limit for Calabi-Yau metrics

2023/05/03 by Yang Li, Li, Yang · 2 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2305.02258

openalex publication_date 2023/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study polarised degenerations of n-dimensional Calabi-Yau hypersurfaces \ F₀F₁… F_m+tF=0\ , where the essential skeleton has dimension 1≤ m≤ n-1. We will describe the limiting behaviour of the Calabi-Yau potential at the C⁰-level, in terms of an optimal transport problem, and in terms of non-archimedean potential theory.

Cited by

• Generic regularity of intermediate complex structure limits
• On multiscale aspects of Kähler-Einstein metrics and algebraic geometry

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