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Published May 2019 | Version Accepted Version
Journal Article Open

The non-archimedean SYZ fibration

Creators

  • 1. ROR icon Imperial College London
  • 2. ROR icon KU Leuven
  • 3. ROR icon Massachusetts Institute of Technology
  • 4. ROR icon Département de Mathématiques

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.

Additional Information

© The Authors 2019. Received 2 February 2018, accepted in final form 22 December 2018, published online 30 April 2019. Johannes Nicaise is supported by the ERC Starting Grant MOTZETA (project 306610) of the European Research Council, and by long term structural funding (Methusalem grant) of the Flemish Government. A part of the research leading to these results was carried out at the Freiburg Institute for Advanced Studies (FRIAS) with funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number 609305. Chenyang Xu is supported by the National Science Fund for Distinguished Young Scholars (11425101), 'Algebraic Geometry'. Tony Yue Yu is supported by the Clay Mathematics Institute.

Attached Files

Accepted Version - 1802.00287.pdf

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1802.00287.pdf

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Additional details

Identifiers

Eprint ID
110828
Resolver ID
CaltechAUTHORS:20210914-164412592

Related works

Describes
10.1112/s0010437x19007152 (DOI)
https://arxiv.org/abs/1802.00287 (URL)

Funding

European Research Council (ERC)
306610
Methusalem
Marie Curie Fellowship
609305
National Science Fund for Distinguished Young Scholars
11425101
Clay Mathematics Institute

Dates

Created
2021-09-14
Created from EPrint's datestamp field
Updated
2021-09-14
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Mathematics Department