Special Lagrangian fibrations, Berkovich retraction, and crystallographic groups
Algebraic Geometry
2022-12-12 v3 Differential Geometry
Number Theory
Abstract
We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties, glue with Berkovich retraction in non-Archimedean geometry by using "hybrid" technique. We also study their symmetries explicitly which can be regarded as crystallographic groups. In particular, a conjecture of Kontsevich-Soibelman is solved at an enhanced level for finite quotients of abelian varieties in any dimension.
Keywords
Cite
@article{arxiv.2206.14474,
title = {Special Lagrangian fibrations, Berkovich retraction, and crystallographic groups},
author = {Keita Goto and Yuji Odaka},
journal= {arXiv preprint arXiv:2206.14474},
year = {2022}
}
Comments
30 pages, v2: added an appendix which discusses a certain limiting process of CY metrics to non-Archimedean CY metric and corrected some typos, v3: corrected some typos and minor mathematical errors