Motivic Zeta Functions for Curve Singularities
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.
Cite
@article{arxiv.0903.1238,
title = {Motivic Zeta Functions for Curve Singularities},
author = {J. J. Moyano-Fernandez and W. A. Zuniga-Galindo},
journal= {arXiv preprint arXiv:0903.1238},
year = {2009}
}
Comments
Several typos and small errors were corrected. The definition of universal zeta function was modified