Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Singularity Theory and Its Applications, S. Izumiya, G. Ishikawa, H. Tokunaga, I. Shimada and T. Sano, eds. (Tokyo: Mathematical Society of Japan, 2006), 421 - 436
An infinitesimal criterion for topological triviality of families of sections of analytic varieties
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.
Received: 6 June 2004
Revised: 16 December 2004
First available in Project Euclid: 3 January 2019
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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