The Alexander polynomial of a plane curve singularity via the ring of   functions on it
  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. 
A.Campillo (Valladolid University, Spain), F.Delgado (Valladolid   University, Spain), S.M.Gusein-Zade (Moscow State Univers...