The Nash problem of arcs and the rational double points D n

Camille Plénat[1]

  • [1] Université de Provence LATP UMR 6632 Centre de Mathématiques et Informatique 39 rue Joliot-Curie 13453 Marseille cedex 13 (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 7, page 2249-2278
  • ISSN: 0373-0956

Abstract

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This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface U with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points D n ( n ≥ 4 ).

How to cite

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Plénat, Camille. "The Nash problem of arcs and the rational double points $D_n$." Annales de l’institut Fourier 58.7 (2008): 2249-2278. <http://eudml.org/doc/10377>.

@article{Plénat2008,
abstract = {This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface $U$ with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points $D_n$ ($n \ge 4$).},
affiliation = {Université de Provence LATP UMR 6632 Centre de Mathématiques et Informatique 39 rue Joliot-Curie 13453 Marseille cedex 13 (France)},
author = {Plénat, Camille},
journal = {Annales de l’institut Fourier},
keywords = {Space of arcs; Nash map; Nash problem; rational double points; space of arcs},
language = {eng},
number = {7},
pages = {2249-2278},
publisher = {Association des Annales de l’institut Fourier},
title = {The Nash problem of arcs and the rational double points $D_n$},
url = {http://eudml.org/doc/10377},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Plénat, Camille
TI - The Nash problem of arcs and the rational double points $D_n$
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 7
SP - 2249
EP - 2278
AB - This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface $U$ with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points $D_n$ ($n \ge 4$).
LA - eng
KW - Space of arcs; Nash map; Nash problem; rational double points; space of arcs
UR - http://eudml.org/doc/10377
ER -

References

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  16. C. Plénat, Résolution du problème des arcs de Nash pour les points doubles rationnels D n ( n ≥ 4 ) ., Note C.R.A.S, Série I 340 (2005), 747-750 Zbl1072.14004MR2141063
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