  We study an analytically irreducible algebroid germ (X, 0) of complex
singularity by considering the filtrations of its analytic algebra, and their
associated graded rings, induced by the divisorial valuations associated to the
irreducible components of the exceptional divisor of the normalized blow-up of
the normalization (Y, 0) of (X, 0), centered at the point 0 of Y. If (X, 0) is
a quasi-ordinary hypersurface singularity, we obtain that the associated graded
ring is an algebra of finite type over the field of complex numbers, namely the
coordinate ring of a non necessarily normal affine toric variety defined by a
semigroup, which is shown to be an analytical invariant of (X, 0). This
provides another proof of the analytical invariance of the normalized
characteristic monomials of (X, 0). If (X, 0) is the algebroid germ of non
necessarily normal toric variety, we apply the same method to prove a local
version of the isomorphism problem for algebroid germs of non necessarily
normal toric varieties.
