Poles of maximal order of motivic zeta functions

Johannes Nicaise, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)217-243
Number of pages27
JournalDuke Mathematical Journal
Volume165
Issue number2
DOIs
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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