Topological finite-determinacy of functions with non-isolated singularities
| dc.creator | de Bobadilla, J. Fernandez | |
| dc.date | 2002-10-17 | |
| dc.date | 2002-12-11 | |
| dc.date.accessioned | 2026-07-07T04:52:04Z | |
| dc.date.available | 2026-07-07T04:52:04Z | |
| dc.description | 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. | |
| dc.description | 26 pages; Main Theorem improved | |
| dc.identifier | https://arxiv.org/abs/math/0210266 | |
| dc.identifier | http://arxiv.org/abs/math/0210266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65331 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32S15, 58K40 | |
| dc.title | Topological finite-determinacy of functions with non-isolated singularities | |
| dc.type | text |