The non-archimedean SYZ fibration

  title={The non-archimedean SYZ fibration},
  author={J. Nicaise and Xu Chen and Tony Yue Yu},
  journal={Compositio Mathematica},
  pages={953 - 972}
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… Expand
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