Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T02:59:18.668Z Has data issue: false hasContentIssue false
  • English
  • Français

Pre-weighted homogeneous map germs—Finite determinacy and topological triviality

Published online by Cambridge University Press:  22 January 2016

Marcelo Jose Saia
Marcelo Jose Saia*
Affiliation:
I.G.C.E.-UNESP, Campus de Rio Claro, C.P.178, R. Claro, S. P. Brasil, 13500-230, [email protected]
Rights & Permissions [Opens in a new window]

Abstract.

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather’s groups A or K) and show that any G-pre-weight ed homogeneous map germ is G-finitely determined. We also give an explicit “order”, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 209 - 220
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Bruce, J. W., Euler characteristics of real varieties, Bull. London Math. Soc., 22, n. 6 (1990), 547–552.CrossRefGoogle Scholar
[2] Bruce, J. W., Ruas, M. A. S. and Saia, M. J., A note on determinacy, Proc. Amer. Math. Soc., 115 (1992), 865–887.CrossRefGoogle Scholar
[3] Damon, J. N., Finite determinacy and topological triviality I, Invent. Math., 62 (1980), 299–324.CrossRefGoogle Scholar
[4] Damon, J. N. and Gaffney, T., Topological triviality of deformations of functions and Newton filtrations, Invent. Math., 72 (1983), 335–358.CrossRefGoogle Scholar
[5] Gaffney, T. and Mond, D. M. Q., Weighted homogeneous maps from the plane to the plane, Math. Proc. Camb. Phil. Soc., 109 (1991), 451–470.CrossRefGoogle Scholar
[6] Kempf, G., Knudsen, F., Munford, D. and Saint-Donat, B., Toroidal embeddings, Lecture Notes in Math., 339 (1973), Springer-Verlag.Google Scholar
[7] Saia, M. J., Poliedros de equisingularidade de germes pre-quase hornogê- neos, Thesis, ICMSC-USP S. Carlos (1991).Google Scholar
[8] Varchenko, A. N., Newton Polyhedra and estimation of oscillating integrals, Funct. Anal. Appl., 10 (1977), 175–196.CrossRefGoogle Scholar
[9] Yoshinaga, E., Topologically principal part of analytic functions, Trans. Amer. Math. Soc., 314, N. 2 (1989), 803–814.CrossRefGoogle Scholar