English

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}
}

Comments

17 pages