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Comptes Rendus Mathématique
Volume 334, n° 4
pages 317-320 (2002)
Doi : S1631-073X(02)02256-2
Received : 20 December 2001 ; 
Sur le nombre de Milnor d'une singularité semi-quasi-homogène
About the Milnor number of a semi-quasi-homogeneous singularity
 

Joël Briançon a , Hélène Maynadier-Gervais b
a Laboratoire J.A. Dieudonné, Université de Nice-Sophia Antipolis, UMR 6621 associée au CNRS, Parc Valrose, 06108 Nice cedex 02, France 
b Laboratoire de mathématiques, Université d'Angers, UMR 6093 associée au CNRS, 2, boulevard Lavoisier, 49045 Angers cedex 01, France 

Note présentée par Bernard Malgrange

Résumé

Soit f =(f 1 ,...,f p ) une famille semi-quasi-homogène de fonctions holomorphes au voisinage de l'origine de Cn. Nous démontrons que f définit une intersection complète à singularité isolée, et nous exprimons le nombre de Milnor de cette singularité comme la colongueur d'un idéal associé naturellement à f . Ceci généralise une formule de G.M. Greuel. Pour citer cet article : J. Briançon, H. Maynadier-Gervais, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 317-320.

The full text of this article is available in PDF format.
Abstract

Let f =(f 1 ,...,f p ) be a semi-quasi-homogeneous family of holomorphic functions in a neighborhood of the origin in Cn. We prove that f defines an isolated complete intersection singularity, and we express the Milnor number of this singularity as the colength of an ideal naturally associated to f . This generalizes a formula due to G.M. Greuel. To cite this article: J. Briançon, H. Maynadier-Gervais, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 317-320.

The full text of this article is available in PDF format.


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