## Advanced Studies in Pure Mathematics

### An infinitesimal criterion for topological triviality of families of sections of analytic varieties

#### Abstract

We present 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 using the integral closure of a convenient ideal as the tangent space to a subset of the set of topologically trivial deformations of a given germ. Applications to the problem of equisingularity of families of sections of $V$ are also discussed.

#### Article information

Dates
Revised: 16 December 2004
First available in Project Euclid: 3 January 2019

https://projecteuclid.org/ euclid.aspm/1546543247

Digital Object Identifier
doi:10.2969/aspm/04310421

Mathematical Reviews number (MathSciNet)
MR2325149

Zentralblatt MATH identifier
1137.32012

#### Citation

Ruas, Maria Aparecida Soares; Tomazella, João Nivaldo. An infinitesimal criterion for topological triviality of families of sections of analytic varieties. Singularity Theory and Its Applications, 421--436, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04310421. https://projecteuclid.org/euclid.aspm/1546543247