Arcs and resolution of singularities

Details Arcs and resolution of singularities Arcs and resolution of singularities

2004-02-06

arxiv.org/abs/math/0402101v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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.

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