Nash [21] proved that every irreducible component of the space of
arcs through a singularity corresponds to an exceptional divisor
that appears 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.
Publié le : 2003-12-01
Classification:
14B05,
14M25,
14J10,
14J17,
14B20
@article{1082137355,
author = {Shihoko Ishii, Shihoko and Koll\'ar, J\'anos},
title = {The Nash problem on arc families of singularities},
journal = {Duke Math. J.},
volume = {120},
number = {3},
year = {2003},
pages = { 601-620},
language = {en},
url = {http://dml.mathdoc.fr/item/1082137355}
}
Shihoko Ishii, Shihoko; Kollár, János. The Nash problem on arc families of singularities. Duke Math. J., Tome 120 (2003) no. 3, pp. 601-620. http://gdmltest.u-ga.fr/item/1082137355/