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On the smallest poles of topological zeta functions

Published online by Cambridge University Press:  04 December 2007

Dirk Segers  and
Willem Veys
Dirk Segers
Affiliation:
K. U. Leuven, Departement Wiskunde, Celestijnenlaan 200B, B-3001 Leuven, [email protected], [email protected]
Willem Veys
Affiliation:
K. U. Leuven, Departement Wiskunde, Celestijnenlaan 200B, B-3001 Leuven, [email protected], [email protected]
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Abstract

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We study the local topological zeta function associated to a complex function that is holomorphic at the origin of $\mathbb{C}^2$ (respectively $\mathbb{C}^3$). We determine all possible poles less than −1/2 (respectively −1). On $\mathbb{C}^2$ our result is a generalization of the fact that the log canonical threshold is never in ]5/6,1[. Similar statements are true for the motivic zeta function.

Keywords

topological zeta functionresolution of singularitieslog canonical threshold14B0514J1732S05 (primary)14E1514H20 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 1 , January 2004 , pp. 130 - 144
Copyright
Foundation Compositio Mathematica 2004