Dans ce travail nous introduisons la notion utile de trivialité modifiée de Nash d’une famille d’ensembles de zéros de germes d’applications polynomiales réelles. Nous donnons d’abord un lemme d’isotopie de Nash permettant d’obtenir la trivialité. Ensuite, à l’aide de ceci, nous montrons deux types de théorèmes de trivialité modifiée de Nash et un théorème de classification finie pour la trivialité.
Ces théorèmes renforcent des résultats topologiques similaires.
In this paper we introduce the notion of modified Nash triviality for a family of zero sets of real polynomial map-germs as a desirable one. We first give a Nash isotopy lemma which is a useful tool to show triviality.
Then, using it, we prove two types of modified Nash triviality theorem and a finite classification theorem for this triviality. These theorems strengthen similar topological results.
@article{AIF_1998__48_5_1395_0,
author = {Fukui, Toshizumi and Koike, Satoshi and Shiota, Masahiro},
title = {Modified Nash triviality of a family of zero-sets of real polynomial mappings},
journal = {Annales de l'Institut Fourier},
volume = {48},
year = {1998},
pages = {1395-1440},
doi = {10.5802/aif.1660},
mrnumber = {99m:14112},
zbl = {0940.14038},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1998__48_5_1395_0}
}
Fukui, Toshizumi; Koike, Satoshi; Shiota, Masahiro. Modified Nash triviality of a family of zero-sets of real polynomial mappings. Annales de l'Institut Fourier, Tome 48 (1998) pp. 1395-1440. doi : 10.5802/aif.1660. http://gdmltest.u-ga.fr/item/AIF_1998__48_5_1395_0/
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