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Motivic zeta functions for curve singularities

Published online by Cambridge University Press:  11 January 2016

J. J. Moyano-Fernández  and
W. A. Zúňiga-Galindo
J. J. Moyano-Fernández
Affiliation:
Institut für Mathematik, Universitát Osnabrück, Albrechtstrasse, 28a 49076 Osnabrück, [email protected]
W. A. Zúňiga-Galindo
Affiliation:
Institut für Mathematik, Universitát Osnabrück, Albrechtstrasse, 28a 49076 Osnabrück, [email protected]
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Abstract

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Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring Op,x at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if Op,x is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.

Keywords

14H2014G1032S4011S40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 198 , June 2010 , pp. 47 - 75
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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