Integration with respect to Euler characteristic over the projectivization of the space of functions and the Alexander polynomial of a plane curve singularity

2000/05/22 by Antonio Campillo, A. Campillo, F. Delgado +5
Mathematics · #14H20 #32S05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Meromorphic and Entire Functions #math.AG #math.GT #msc:14H20 #msc:32S05

paper · pdf · doi:10.48550/arxiv.math/0005206

arxiv created 2000/05/22 · openalex publication_date 2000/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss a notion of integration with respect to the Euler characteristic in the projectivization ¶\cal O_\Cⁿ,0 of the ring \cal O_\Cⁿ,0 of germs of functions on Cⁿ and show that the Alexander polynomial and the zeta-function of a plane curve singularity can be expressed as certain integrals over ¶\cal O_\C²,0 with respect to the Euler characteristic.

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