Completion of the moduli space for polarized Calabi-Yau manifolds

2014/10/11 by Yuguang Zhang, Zhang, Yuguang
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1410.2979

openalex publication_date 2014/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct a completion of the moduli space for polarized Calabi-Yau manifolds by using Ricci-flat Kähler-Einstein metrics and the Gromov-Hausdorff topology, which parameterizes certain Calabi-Yau varieties. We then study the algebro-geometric perperties and the Weil-Petersson geometry of such completion. We show that the completion can be exhausted by sequences of quasi-projective varieties, and new points added have finite Weil-Petersson distance to the interior.

Citations

• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• Singular Kahler-Einstein metrics

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