Non-archimedean periods for log Calabi-Yau surfaces

2025/06/02 by Soham Karwa, Jonathan Lai, Karwa, Soham +1
Mathematics · #14C30 #14G22 #14J10 #14J26 #14T90 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2506.01651

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the first instance of a conjecture by Kontsevich-Soibelman that the non-archimedean period map recovers the analytic periods in the case of log Calabi-Yau surfaces. In particular, we show that the K-affine structure, a natural enhancement of the singular integral affine structure on the essential skeleton, determines the isomorphism type of the log Calabi-Yau surface.

Citations

• The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus
• Period integrals from wall structures via tropical cycles, canonical\n coordinates in mirror symmetry and analyticity of toric degenerations
• The non-archimedean SYZ fibration
• Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I
• Skeletons and tropicalizations
• Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton
• A guide to tropicalizations
• Mirror symmetry for log Calabi-Yau surfaces I
• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Related

• Mirror Symmetry for log Calabi-Yau Surfaces II
• Tropical Periods for Calabi-Yau Hypersurfaces in non--Fano Toric Varieties
• Periods of tropical Calabi--Yau hypersurfaces
• Construction of non-Kähler Calabi-Yau manifolds by log deformations
• Log Calabi-Yau mirror symmetry and non-archimedean disks