# Motivic zeta functions of degenerating Calabi-Yau varieties

## TL;DR

This paper investigates motivic zeta functions of degenerating Calabi-Yau varieties, establishing conditions under which they satisfy a monodromy conjecture and linking them to non-archimedean geometry and mirror symmetry.

## Contribution

It proves that motivic zeta functions satisfy an analog of Igusa's monodromy conjecture under Galois-equivariant Kulikov models and relates these functions to the skeleton in non-archimedean geometry.

## Key findings

- Motivic zeta functions satisfy the monodromy conjecture in certain cases.
- Established a relation between zeta functions and the skeleton in non-archimedean geometry.
- Provided examples verifying the Galois-equivariant Kulikov model condition.

## Abstract

We study motivic zeta functions of degenerating families of Calabi-Yau varieties. Our main result says that they satisfy an analog of Igusa's monodromy conjecture if the family has a so-called Galois-equivariant Kulikov model; we provide several classes of examples where this condition is verified. We also establish a close relation between the zeta function and the skeleton that appeared in Kontsevich and Soibelman's non-archimedean interpretation of the SYZ conjecture in mirror symmetry.