The Nash problem on arc families of singularities
Algebraic Geometry
2007-05-23 v2
Abstract
Nash proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that occurs on every resolution. He asked if the converse also holds: does every such exceptional divisor correspond to an arc family? We prove that the converse holds for toric singularities but fails in general.
Keywords
Cite
@article{arxiv.math/0207171,
title = {The Nash problem on arc families of singularities},
author = {Shihoko Ishii and János Kollár},
journal= {arXiv preprint arXiv:math/0207171},
year = {2007}
}
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17 pages