  For a certain class of varieties X, we derive a formula for the valuation
d_{X} on the arc space L(Y) of a smooth ambient space Y, in terms of an
embedded resolution of singularities. A simple transformation rule yields a
formula for the geometric Poincare series. Furthermore, we prove that for this
class of varieties, the arithmetic and the geometric Poincare series coincide.
We also study the geometric valuation for plane curves.
