We prove two formulae that express the Alexander polynomial
$\Delta\sp C$ of several variables of a plane curve singularity $C$ in
terms of the ring $\mathscr {O}\sb C$ of germs of analytic functions
on the curve. One of them expresses $\Delta\sp C$ in terms of
dimensions of some factors corresponding to a (multi-indexed)
filtration on the ring $\mathscr {O}\sb C$. The other one gives the
coefficients of the Alexander polynomial $\Delta\sp C$ as Euler
characteristics of some explicitly described spaces (complements to
arrangements of projective hyperplanes).