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June 2015 Deformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularities
Christophe Eyral, Maria Aparecida Soares Ruas
Nagoya Math. J. 218: 29-50 (June 2015). DOI: 10.1215/00277630-2847026


We show that the possible jump of the order in an 1-parameter deformation family of (possibly nonisolated) hypersurface singularities, with constant Lê numbers, is controlled by the powers of the deformation parameter. In particular, this applies to families of aligned singularities with constant topological type—a class for which the Lê numbers are “almost” constant. In the special case of families with isolated singularities—a case for which the constancy of the Lê numbers is equivalent to the constancy of the Milnor number—the result was proved by Greuel, Plénat, and Trotman.

As an application, we prove equimultiplicity for new families of nonisolated hypersurface singularities with constant topological type, answering partially the Zariski multiplicity conjecture.


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Christophe Eyral. Maria Aparecida Soares Ruas. "Deformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularities." Nagoya Math. J. 218 29 - 50, June 2015.


Published: June 2015
First available in Project Euclid: 11 December 2014

zbMATH: 06451293
MathSciNet: MR3345623
Digital Object Identifier: 10.1215/00277630-2847026

Primary: 32S15
Secondary: 32S05 , 32S25

Keywords: deformations with constant Lê numbers , hypersurface singularities , multiplicities , Thom’s $a_{f}$ condition , Zariski’s multiplicity conjecture

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal


Vol.218 • June 2015
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