  To a plane curve singularity one associates a multi-index filtration on the
ring of germs of functions of two variables defined by the orders of a function
on irreducible components of the curve. The Poincare series of this filtration
turnes out to coincide with the Alexander polynomial of the curve germ. For a
finite set of divisorial valuations on the ring corresponding to some
components of the exceptional divisor of a modification of the plane, in a
previous paper there was obtained a formula for the Poincare series of the
corresponding multi-index filtration similar to the one associated to plane
germs. Here we show that the Poincare series of a set of divisorial valuations
on the ring of germs of functions of two variables defines "the topology of the
set of the divisors" in the sense that it defines the minimal resolution of
this set up to combinatorial equivalence. For the plane curve singularity case,
we also give a somewhat simpler proof of the statement by Yamamoto which proves
that the Alexander polynomial is equivalent to the embedded topology.
