## Nagoya Mathematical Journal

### Topological triviality of families of functions on analytic varieties

#### Abstract

We present in this paper sufficient conditions for the topological triviality of families of germs of functions defined on an analytic variety $V$. The main result is an infinitesimal criterion based on a convenient weighted inequality, similar to that introduced by T. Fukui and L. Paunescu. When $V$ is a weighted homogeneous variety, we obtain as a corollary, the topological triviality of deformations by terms of non negative weights of a weighted homogeneous germ consistent with $V$. Application of the results to deformations of Newton non-degenerate germs with respect to a given variety is also given.

#### Article information

Source
Nagoya Math. J., Volume 175 (2004), 39-50.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114632093

Mathematical Reviews number (MathSciNet)
MR2085309

Zentralblatt MATH identifier
1080.32027

#### Citation

Ruas, Maria Aparecida Soares; Tomazella, João Nivaldo. Topological triviality of families of functions on analytic varieties. Nagoya Math. J. 175 (2004), 39--50. https://projecteuclid.org/euclid.nmj/1114632093

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