Topological finite-determinacy of functions with non-isolated singularities |
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Authors: | Email author" target="_blank">Javier?Fernández de BobadillaEmail author |
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Institution: | (1) Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508TA Utrecht, The Netherlands |
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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. |
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Keywords: | Primary 32S15 58K40 |
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