Arcs, valuations and the Nash map
Algebraic Geometry
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0410526,
title = {Arcs, valuations and the Nash map},
author = {Shihoko Ishii},
journal= {arXiv preprint arXiv:math/0410526},
year = {2007}
}
Comments
One wrong statement in Theorem 3.6 was deleted. This does not affect the rest of this paper