Integration with respect to Euler characteristic over the projectivization of the space of functions and the Alexander polynomial of a plane curve singularity
Abstract
We discuss a notion of integration with respect to the Euler characteristic in the projectivization $¶{\cal O}_{\C^n,0}$ of the ring ${\cal O}_{\C^n,0}$ of germs of functions on $C^n$ and show that the Alexander polynomial and the zetafunction of a plane curve singularity can be expressed as certain integrals over $¶{\cal O}_{\C^2,0}$ with respect to the Euler characteristic.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2000
 arXiv:
 arXiv:math/0005206
 Bibcode:
 2000math......5206C
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Geometric Topology;
 32S05;
 14H20