Motivic Zeta Functions for Curve Singularities

Details Motivic Zeta Functions for Curve Singularities Motivic Zeta Functions for Curve Singularities

2009-03-06

arxiv.org/abs/0903.1238v3

Mathematics

Algebraic Geometry

Several typos and small errors were corrected. The definition of universal zeta function was modified

Scientific paper

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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