Soit la décomposition canonique de l’espace des arcs 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’est pas inclus dans . On applique ces conditions pour donner deux nouvelles preuves du problème de Nash pour les singularités sandwich minimales.
Let 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 is not included in . These conditions allow us to give two different direct demonstration of Nah problem for minimal sandwiched singularities.
Classification : 14J17
Mots clés : géométrie algébrique, espace des arcs, singularités sandwichs minimales, problème de 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}, pages = {805--823}, publisher = {Association des Annales de l'institut Fourier}, volume = {55}, number = {3}, year = {2005}, doi = {10.5802/aif.2115}, zbl = {1080.14021}, mrnumber = {2149404}, language = {fr}, url = {http://www.numdam.org/item/AIF_2005__55_3_805_0/} }
Plénat, Camille. A propos du problème des arcs de Nash. Annales de l'Institut Fourier, Tome 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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