The non-archimedean SYZ fibration

2019/04/30 by Johannes Nicaise, Chenyang Xu, Tony Yue Yu · 3 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · doi:10.1112/s0010437x19007152

Abstract

We construct non-archimedean SYZ (Strominger–Yau–Zaslow) fibrations for maximally degenerate Calabi–Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

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• Tropical reductive groups and principal bundles on metric graphs
• Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties
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