Arcs, valuations and the Nash map

Details Arcs, valuations and the Nash map Arcs, valuations and the Nash map

2004-10-25

arxiv.org/abs/math/0410526v2

Mathematics

Algebraic Geometry

One wrong statement in Theorem 3.6 was deleted. This does not affect the rest of this paper

Scientific paper

This paper gives a map from the set of families of arcs on a variety to the set of valuations on the rational function field of the variety We characterize a family of arcs which corresponds to a divisorial valuation by this map. We can see that both the Nash map and a certain McKay correspondence are the restrictions of this map. This paper also gives the affirmative answer to the Nash problem for a non-normal variety in a certain category. As a corollary, we get the affirmative answer for a non-normal toric variety.

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