Toric geometry and integral affine structures in non-archimedean mirror symmetry
Abstract
We study integral dlt models of a proper C((t))-variety X along a toric stratum of the special fiber. We prove that the associated Berkovich retraction - from the non-archimedean analytification of X onto the dual complex of the model - is an affinoid torus fibration around the simplex corresponding to the toric stratum, which extends results from Nicaise-Xu-Yu. This allows us to construct new types of non-archimedean retractions for maximally degenerate families of quartic K3 surfaces and quintic 3-folds, by gluing several non-archimedean SYZ fibrations, each one toric along a codimension one stratum. We then show that the new retractions induce the same singular integral affine structures that arise on the dual complex of toric degenerations in the Gross-Siebert program, as well as on the Gromov-Hausdorff limit of the family.
Keywords
Cite
@article{arxiv.2110.04223,
title = {Toric geometry and integral affine structures in non-archimedean mirror symmetry},
author = {Enrica Mazzon and Léonard Pille-Schneider},
journal= {arXiv preprint arXiv:2110.04223},
year = {2023}
}