The Nash problem of arcs and the rational double points D n
Annales de l'Institut Fourier, Volume 58 (2008) no. 7, pp. 2249-2278.

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).

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 .

DOI: 10.5802/aif.2413
Classification: 14B05,  14J17
Keywords: Space of arcs, Nash map, Nash problem, rational double points
Plénat, Camille 1

1 Université de Provence LATP UMR 6632 Centre de Mathématiques et Informatique 39 rue Joliot-Curie 13453 Marseille cedex 13 (France)
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Plénat, Camille. The Nash problem of arcs and the rational double points $D_n$. Annales de l'Institut Fourier, Volume 58 (2008) no. 7, pp. 2249-2278. doi : 10.5802/aif.2413. http://www.numdam.org/articles/10.5802/aif.2413/

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