Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture

2024/07/12 by Keita Goto, Yuto Yamamoto, Goto, Keita +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2407.09133

openalex publication_date 2024/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a toric degeneration X of Calabi--Yau complete intersections of Batyrev--Borisov in the Gross--Siebert program. For the toric degeneration X, we study the real Monge--Ampère equation corresponding to the non-archimedean Monge--Ampère equation that yields the non-archimedean Calabi--Yau metric. Our main theorem describes the real Monge--Ampère equation in terms of tropical geometry and proves the metric SYZ conjecture for the toric degeneration X supposing the existence of its solution.

Cited by

• Degeneration of Calabi-Yau metrics and canonical basis

Related

• Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces
• Non-archimedean SYZ fibrations via tropical contractions
• Metric SYZ conjecture for certain toric Fano hypersurfaces
• Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi-Yau hypersurfaces
• Mixed toric residues and tropical degenerations