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