[A solution to the Nash problem of arcs for rational double points ]
This Note deals with the Nash problem, which claims that there are as many families of arcs on a singular germ of surface U as there are essential components of the exceptional divisor in the desingularisation of this singularity. We prove that this claim holds for the rational double points .
Cette Note a pour objet le problème des arcs de Nash, selon lequel il y aurait autant de familles d'arcs sur un germe de surface singulier U que de composantes essentielles d'une désingularisation de cette singularité. On résout le problème par l'affirmative pour les points doubles rationnels .
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Camille Plénat 1
@article{CRMATH_2005__340_10_747_0, author = {Camille Pl\'enat}, title = {R\'esolution du probl\`eme des arcs de {Nash} pour les points doubles rationnels $ {D}_{n}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {747--750}, publisher = {Elsevier}, volume = {340}, number = {10}, year = {2005}, doi = {10.1016/j.crma.2005.04.023}, language = {fr}, }
Camille Plénat. Résolution du problème des arcs de Nash pour les points doubles rationnels $ {D}_{n}$. Comptes Rendus. Mathématique, Volume 340 (2005) no. 10, pp. 747-750. doi : 10.1016/j.crma.2005.04.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.023/
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