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26 April 2024

» arxiv » math.AG/0005206

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Integration with respect to Euler characteristic over the projectivization of the space of functions and the Alexander polynomial of a plane curve singularity
A.Campillo ; F.Delgado ; S.M.Gusein-Zade ;
Date:	22 May 2000
Subject:	Algebraic Geometry; Geometric Topology MSC-class: 32S05; 14H20 \| math.AG math.GT
Affiliation:	University of Valladolid, Spain), F.Delgado (University of Valladolid, Spain), S.M.Gusein-Zade (Moscow State University, Russia
Abstract:	We discuss a notion of integration with respect to the Euler characteristic in the projectivization $P{cal O}_{C^n,0}$ of the ring ${cal O}_{C^n,0}$ of germs of functions on $C^n$ and show that the Alexander polynomial and the zeta-function of a plane curve singularity can be expressed as certain integrals over $P{cal O}_{C^2,0}$ with respect to the Euler characteristic.
Source:	arXiv, math.AG/0005206
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