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

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

arxiv.org/abs/math/0005206v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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