The non-archimedean SYZ fibration

Johannes Nicaise, Chenyang Xu, Tony Yue Yu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)953-972
Number of pages20
JournalCompositio Mathematica
Volume155
Issue number5
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Strominger-Yau-Zaslow conjecture
  • minimal model program
  • mirror symmetry
  • non-archimedean geometry

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