Motivic zeta functions of degenerating Calabi–Yau varieties

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.