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Comptes Rendus Mathématique
Volume 341, n° 6
pages 357-360 (septembre 2005)
Doi : 10.1016/j.crma.2005.06.033
Received : 1 Mars 2005 ;  accepted : 28 June 2005
On the Łojasiewicz numbers, II
Sur les nombres de Łojasiewicz, II
 

Evelia García Barroso a , Tadeusz Krasiński b , Arkadiusz Płoski c
a Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain 
b Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland 
c Department of Mathematics, Technical University, Al. 1000 L PP7, 25-314 Kielce, Poland 

Abstract

For every holomorphic function in two complex variables with an isolated critical point at the origin we consider the Łojasiewicz exponent   defined to be the smallest   such that   near   for some  . The numbers   are rational. In this Note we discuss the interplay between arithmetical properties of the rationals   and topological properties of plane curve singularities  . To cite this article: E. García Barroso et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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Résumé

Pour toute fonction holomorphe f de deux variables complexes ayant un point critique isolé à lʼorigine nous considérons lʼexposant de Łojasiewicz   égal, par definition, au plus petit nombre   tel que   dans un voisinage de  . Dans cette Note nous étudions le rapport entre des propriétés arithmétiques de lʼexposant   et des propriétés topologiques de la singularité plane  . Pour citer cet article : E. García Barroso et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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


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