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Modified Nash triviality of a family of zero-sets of real polynomial mappings. (English) Zbl 0940.14038
Summary: 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.

##### MSC:
 14P20 Nash functions and manifolds 58A07 Real-analytic and Nash manifolds 58K20 Algebraic and analytic properties of mappings on manifolds 14P10 Semialgebraic sets and related spaces 14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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