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arXiv · 1701.09155

Motivic zeta functions of degenerating Calabi-Yau varieties

Lars Halvard Halle·Johannes Nicaise
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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.

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Lars Halvard Halle, Johannes Nicaise. 2017-01-31. Motivic zeta functions of degenerating Calabi-Yau varieties. https://arxiv.org/abs/1701.09155

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