JournalscmhVol. 79, No. 4pp. 659–688

Topological finite-determinacy of functions with non-isolated singularities

  • Javier Fernández de Bobadilla

    University of Utrecht, Netherlands
Topological finite-determinacy of functions with non-isolated singularities cover
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Abstract

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.

Cite this article

Javier Fernández de Bobadilla, Topological finite-determinacy of functions with non-isolated singularities. Comment. Math. Helv. 79 (2004), no. 4, pp. 659–688

DOI 10.1007/S00014-004-0813-1