Metric SYZ conjecture for certain toric Fano hypersurfaces

2023/01/30 by Yang Li, Li, Yang · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Class (philosophy) #Combinatorics #Computer science #Conjecture #Differential Geometry (math.DG) #FOS: Mathematics #Fano plane #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Metric (unit) #Polytope #Pure mathematics #Symmetry (geometry) #Toric variety

paper · pdf · doi:10.48550/arxiv.2301.12983

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We prove the metric version of the SYZ conjecture for a class of Calabi-Yau hypersurfaces inside toric Fano manifolds, by solving a variational problem whose minimizer may be interpreted as a global solution of the real Monge-Ampère equation on certain polytopes. This does not rely on discrete symmetry.

Cited by

• Generic regularity of intermediate complex structure limits
• Degeneration of Calabi-Yau metrics and canonical basis

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