arXiv:math/0205111 [math.AG]AbstractReferencesReviewsResources
The Alexander polynomial of a plane curve singularity via the ring of functions on it
A. Campillo, F. Delgado, S. M. Gusein-Zade
Published 2002-05-10Version 1
We prove 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 factors 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 final version of this article will be published in the Duke Mathematical Journal.
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