The non-archimedean SYZ fibration

TL;DR

This paper constructs non-archimedean SYZ fibrations for maximally degenerate Calabi-Yau varieties, confirming a prediction by Kontsevich and Soibelman, and describes the affine structure on the base explicitly.

Contribution

It provides a new construction of non-archimedean SYZ fibrations and analyzes their structure, advancing understanding of Calabi-Yau degenerations.

Findings

Fibrations are affinoid torus fibrations outside a codimension two subset.

Explicit description of the integral affine structure on the base.

Confirmation of Kontsevich and Soibelman's prediction.

Abstract

We construct non-archimedean SYZ 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-models along one-dimensional strata.