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Original Articles
A Numerical Characterization of Equisingularity for Map Germs from N-Space, (N≥3), to the Plane
Terence GaffneyProfessor of Mathematics Northeastern UniversityBostonView full profile → , Ranjit VohraMassachusetts Board of Higher EducationP.O. Box 491Bridgewater, MA, 02324, U.S.A.View full profile →
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- Received:
- 06 Oct 2003
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2004.10698479
- Pages:
- 43–55
Abstract
By a celebrated 1976 result regarding the geometry of families of hypersurfaces with isolated singularities, Lê and Ramanujam showed that the constancy of a single numerical invariant, namely the Milnor number, implies that the family is locally topologically trivial. This classical result has led to generalizations of the Milnor number to various numerical invariants, including ”polar multiplicities”, ”Lê numbers” and ”Segre numbers”, all designed to reflect the geometry of singularities in very general scenarios. In the present study, we consider families of finitely-determined holomorphic map germs from Cundefined to C2 for n ≥ 3, and characterize local topological triviality in terms of the constancy of (n-1) Lê numbers.
Keywords
References
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