Arcs and resolution of singularities
Abstract
For a certain class of varieties X, we derive a formula for the valuation dX 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.
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