Translator Disclaimer
1 February 2016 Poles of maximal order of motivic zeta functions
Johannes Nicaise, Chenyang Xu
Duke Math. J. 165(2): 217-243 (1 February 2016). DOI: 10.1215/00127094-3165648

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.

Citation

Download Citation

Johannes Nicaise. Chenyang Xu. "Poles of maximal order of motivic zeta functions." Duke Math. J. 165 (2) 217 - 243, 1 February 2016. https://doi.org/10.1215/00127094-3165648

Information

Received: 26 March 2014; Revised: 22 January 2015; Published: 1 February 2016
First available in Project Euclid: 19 January 2016

zbMATH: 1366.14008
MathSciNet: MR3457672
Digital Object Identifier: 10.1215/00127094-3165648

Subjects:
Primary: 14E30
Secondary: 14B05, 14D06, 14E18, 14G22

Rights: Copyright © 2016 Duke University Press

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.165 • No. 2 • 1 February 2016
Back to Top