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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
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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 zeta-function of a plane curve singularity can be expressed as certain integrals over $¶{\cal O}_{\C^2,0}$ with respect to the Euler characteristic.

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A. Campillo, F. Delgado, S. M. Gusein-Zade. 2000-05-22. Integration with respect to Euler characteristic over the projectivization of the space of functions and the Alexander polynomial of a plane curve singularity. https://arxiv.org/abs/math/0005206

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