A propos du problème des arcs de Nash  [ On Nash problem of arc ]
Annales de l'Institut Fourier, Volume 55 (2005) no. 3, p. 805-823

Let ℋ=⋃N i the canonical decomposition of the space of arcs passing through a normal surface singularity. In this paper, we give two new conditions to ensure that N i is not included in N j . These conditions allow us to give two different direct demonstration of Nah problem for minimal sandwiched singularities.

Soit ℋ=⋃N i la décomposition canonique de l’espace des arcs ℋ passant par une singularité normale de surface. Dans cet article, on propose deux nouvelles conditions qui si elles sont vérifiées permettent de montrer que N i n’est pas inclus dans N j . On applique ces conditions pour donner deux nouvelles preuves du problème de Nash pour les singularités sandwich minimales.

DOI : https://doi.org/10.5802/aif.2115
Classification:  14J17
Keywords: geometry algebraic, space of arcs, minimal sandwiched singularities, problem of Nash 
@article{AIF_2005__55_3_805_0,
     author = {Pl\'enat, Camille},
     title = {A propos du probl\`eme des arcs de Nash},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {3},
     year = {2005},
     pages = {805-823},
     doi = {10.5802/aif.2115},
     zbl = {1080.14021},
     mrnumber = {2149404},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2005__55_3_805_0}
}

A propos du problème des arcs de Nash. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 805-823. doi : 10.5802/aif.2115. http://www.numdam.org/item/AIF_2005__55_3_805_0/

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