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Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi-Yau hypersurfaces

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arxiv 2210.05578 v2 pith:LUHP7XDP submitted 2022-10-11 math.AG math.DG

Léonard Pille-Schneider This is my paper
classification math.AGmath.DG
keywords hypersurfacesnon-archimedeantoriccalabi-yaufibrationhybridspacealong
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Using a construction by Yamamoto of tropical contractions, we construct a non-archimedean SYZ fibration on the Berkovich analytification of a class of maximally degenerate hypersurfaces in projective space. We furthermore prove that under a discrete symmetry assumption, the potential for the non-archimedean Calabi-Yau metric is constant along the fibers of the retraction. The proof uses the work of Li on the Fermat degeneration of hypersurfaces, and an explicit description of toric plurisubharmonic metrics on the hybrid space associated to a complex toric variety.

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  1. Generic regularity of intermediate complex structure limits

    math.DG 2025-11 conditional novelty 7.0 of 10

    For intermediate complex structure limits of Calabi-Yau degenerations, the collapsing Ricci-flat metrics converge in C^0 (and in stretched coordinates C^∞) to the non-archimedean ansatz metric on the generic region.

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