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 0. 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 nonarchimedean analytification of the degeneration towards the Kontsevich–Soibelman skeleton.
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