Commentarii Mathematici Helvetici


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Volume 79, Issue 4, 2004, pp. 659–688
DOI: 10.1007/s00014-004-0813-1

Published online: 2004-12-31

Topological finite-determinacy of functions with non-isolated singularities

Javier Fernández de Bobadilla[1]

(1) University of Utrecht, Netherlands

We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the following statement which generalizes classical results of Thom and Varchenko: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged under a deformation within the ideal that only modifies sufficiently large order terms of the Taylor expansion. Then A has infinite codimension in I in a suitable sense. We also prove the existence of generic topological types of families of germs of I parametrized by an irreducible analytic set.

Keywords: non-isolated singularities, topological finite-determinacy, discriminants

Fernández de Bobadilla Javier: Topological finite-determinacy of functions with non-isolated singularities. Comment. Math. Helv. 79 (2004), 659-688. doi: 10.1007/s00014-004-0813-1