Motivic Zeta Functions for Curve Singularities

2009/03/06 by Moyano-Fernandez, J. J., Zuniga-Galindo, W. A. · 1 citation
#11S40 (Secondary) #14G10 (Primary) #14H20 #32S40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0903.1238

Abstract

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring O_P,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 O_P,X is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincare 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 Poincare series introduced by Campillo, Delgado and Gusein-Zade.

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