The Alexander Polynomial of a Plane Curve Singularity via the Ring of Functions on It
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چکیده
We prove two formulae that express the Alexander polynomial 1C of several variables of a plane curve singularity C in terms of the ring OC of germs of analytic functions on the curve. One of them expresses1C in terms of dimensions of some factors corresponding to a (multi-indexed) filtration on the ring OC . The other one gives the coefficients of the Alexander polynomial 1C as Euler characteristics of some explicitly described spaces (complements to arrangements of projective hyperplanes).
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تاریخ انتشار 2002