Nagoya Mathematical Journal

Topological triviality of families of functions on analytic varieties

Maria Aparecida Soares Ruas and João Nivaldo Tomazella

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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

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114632093

Mathematical Reviews number (MathSciNet)
MR2085309

Zentralblatt MATH identifier
1080.32027

Subjects
Primary: 32S15: Equisingularity (topological and analytic) [See also 14E15]
Secondary: 58Kxx: Theory of singularities and catastrophe theory [See also 32Sxx, 37- XX]

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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