The non-archimedean SYZ fibration
OA Location
Author(s)
Nicaise, Johannes
Xu, Chenyang
Yu, Tony Yue
Type
Journal Article
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.
Date Issued
2019-05-01
Date Acceptance
2018-12-22
Citation
Compositio Mathematica, 2019, 155 (5), pp.953-972
ISSN
0010-437X
Publisher
Foundation Compositio Mathematica
Start Page
953
End Page
972
Journal / Book Title
Compositio Mathematica
Volume
155
Issue
5
Copyright Statement
© 2019 The Authors. This article has been published in a revised form in Compositio Mathematica [https://doi.org/10.1112/S0010437X19007152]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Sponsor
Commission of the European Communities
Identifier
http://arxiv.org/abs/1802.00287v2
Grant Number
306610
Subjects
math.AG
math.AG
Notes
Grant information completed; no changes to the remainder of the paper
Publication Status
Published
Date Publish Online
2019-04-30