A. Campillo, F. Delgado, S. M. Gusein-Zade
Published 2000-02-07Version 1
We give two formulae which express the Alexander polynomial $\Delta^C$ of several variables of a plane curve singularity $C$ in terms of the ring ${\cal O}_{C}$ of germs of analytic functions on the curve. One of them expresses $\Delta^C$ in terms of dimensions of some factorspaces corresponding to a (multi-indexed) filtration on the ring ${\cal O}_{C}$. The other one gives the coefficients of the Alexander polynomial $\Delta^C$ as Euler characteristics of some explicitly described spaces (complements to arrangements of projective hyperplanes).
The Alexander polynomial of a plane curve singularity via the ring of functions on it
Integration with respect to Euler characteristic over the projectivization of the space of functions and the Alexander polynomial of a plane curve singularity
The minimal Tjurina number of irreducible germs of plane curve singularities
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