The non-archimedean SYZ fibration

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 desc...

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Bibliographic Details
Published in:Compositio mathematica 2019-05, Vol.155 (5), p.953-972
Main Authors: Nicaise, Johannes, Xu, Chenyang, Yu, Tony Yue
Format: Article
Language:English
Subjects:
Algebra
Algebraic Geometry
Geometry
Mathematics
Symmetry
Toruses
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Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X19007152