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Modified Nash triviality of a family of zero-sets of real polynomial mappings

Toshizumi Fukui;  Satoshi Koike;  Masahiro Shiota — 1998

Annales de l'institut Fourier

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.

Constructing blow-analytic isomorphisms

Toshizumi Fukui;  Tzee-Char Kuo;  Laurentiu Paunescu — 2001

Annales de l’institut Fourier

In this paper we construct non-trivial examples of isomorphisms and we obtain, via toric modifications, an inverse function theorem in this category. We also show that any analytic curve in ℝ n , n ≥ 3 , can be deformed via a rational blow- analytic isomorphism of ℝ n , to a smooth analytic arc.

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