The Nash problem of arcs and the rational double points D n  [ Résolution du problème de Nash pour les singularités D n  ]
Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2249-2278.

Dans cet article, on étudie le problème des arcs de Nash, qui consiste à comparer le nombre de composantes irréductibles de l’espace des arcs passant par une singularité isolée de surface normale avec les courbes exceptionnelles apparaissant dans la résolution minimale de cette singularité. On montre que les deux nombres sont égaux dans le cas des points doubles rationnels D n .

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 (n4).

DOI : https://doi.org/10.5802/aif.2413
Classification : 14B05,  14J17
Mots clés : espace des arcs, problème de Nash, points doubles rationnels
@article{AIF_2008__58_7_2249_0,
     author = {Pl\'enat, Camille},
     title = {The Nash problem of arcs and the rational double points $D\_n$},
     journal = {Annales de l'Institut Fourier},
     pages = {2249--2278},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {7},
     year = {2008},
     doi = {10.5802/aif.2413},
     mrnumber = {2498350},
     zbl = {1168.14004},
     language = {en},
     url = {http://archive.numdam.org/item/AIF_2008__58_7_2249_0/}
}
Plénat, Camille. The Nash problem of arcs and the rational double points $D_n$. Annales de l'Institut Fourier, Tome 58 (2008) no. 7, pp. 2249-2278. doi : 10.5802/aif.2413. http://archive.numdam.org/item/AIF_2008__58_7_2249_0/

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