Nagoya Mathematical Journal

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 $\mathcal{O}_{P,X}$ 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 $\mathcal{O}_{P,X}$ 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.

Article information

Source
Nagoya Math. J., Volume 198 (2010), 47-75.

Dates
First available in Project Euclid: 10 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1273496985

Digital Object Identifier
doi:10.1215/00277630-2009-007

Mathematical Reviews number (MathSciNet)
MR2666577

Zentralblatt MATH identifier
1252.14019

Citation

Moyano-Fernández, J. J.; Zúñiga-Galindo, W. A. Motivic zeta functions for curve singularities. Nagoya Math. J. 198 (2010), 47--75. doi:10.1215/00277630-2009-007. https://projecteuclid.org/euclid.nmj/1273496985

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