Poles of maximal order of motivic zeta functions

Abstract

We prove a 1999 conjecture of Veys, which says that the opposite of the log canonical threshold is the only possible pole of maximal order of Denef and Loeser's motivic zeta function associated with a germ of a regular function on a smooth variety over a field of characteristic zero. We apply similar methods to study the weight function on the Berkovich skeleton associated with a degeneration of Calabi-Yau varieties. Our results suggest that the weight function induces a flow on the non-archimedean analytification of the degeneration towards the Kontsevich-Soibelman skeleton.

to appear in Duke Mathematical Journal

References in corpus (3)

• The essential skeleton of a degeneration of algebraic varieties
• An introduction to $p$-adic and motivic zeta functions and the monodromy conjecture
• Berkovich skeleta and birational geometry

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• Interaction Between Singularity Theory and the Minimal Model Program
• Uniform rationality of Poincaré series of p-adic equivalence relations and Igusa's conjecture on exponential sums
• On the motivic oscillation index and bound of exponential sums modulo $p^m$ via analytic isomorphisms
• Motivic zeta function of the Hilbert schemes of points on a surface