The Alexander polynomial of a plane curve singularity via the ring of functions on itстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:We prove two formulae that express the Alexander polynomial of several variables of a plane curve singularity $C$ in terms of the ring $O_C$ of germs of analytic functions on the curve. One of them expresses the Alexander polynomial in terms of dimensions of some factors corresponding to a (multi-indexed) filtration on the ring $O_C$. The other one gives the coefficients of the Alexander polynomial as Euler characteristics of some explicitly described spaces (complements to arrangements of projective hyperplanes).