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Geometric determination of the Poles of Highest and second Highest order of Hodge And motivic Zeta functions

Published online by Cambridge University Press:  22 January 2016

B. Rodrigues
B. Rodrigues*
Affiliation:
Departement Wiskunde, Celestijnenlaan, 200B, 3001, Leuven, Belgium. bart.rodrigues@wis.kuleuven.ac.be
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Abstract

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To any f ∈ ℂ[x 1, … ,xn ] \ ℂ with f(0) = 0 one can associate the motivic zeta function. Another interesting singularity invariant of f -1{0} is the zeta function on the level of Hodge polynomials, which is actually just a specialization of the motivic one. In this paper we generalize for the Hodge zeta function the result of Veys which provided for n = 2 a complete geometric determination of the poles. More precisely we give in arbitrary dimension a complete geometric determination of the poles of order n − 1 and n. We also show how to obtain the same results for the motivic zeta function.

Keywords

14B0514E1514J1732S45

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 176 , 2004 , pp. 1 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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