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Comptes Rendus Mathématique
Volume 339, n° 2
pages 131-136 (juillet 2004)
Doi : 10.1016/j.crma.2004.04.022
Received : 2 October 2003 ;  accepted : 29 April 2004
Sur les tissus plans de rang maximal et le problème de Chern
On maximal rank planar webs and Chern's problem

Luc  Pirio
Équipe d'analyse complexe, institut de mathématique de Jussieu, 175, rue du Chevaleret, 75013 Paris, France 

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On explique comment il est possible d'obtenir des conditions nécessaires sur des fonctions définissant un germe de tissu plan, pour que celui-ci soit de rang maximal. On applique ensuite cette méthode à l'étude des 5-tissus plans de rang maximal. On montre l'existence d'autres 5-tissus exceptionnels que le tissu de Bol, apportant ainsi une réponse au problème de Chern. Pour citer cet article : L. Pirio, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

Abstract

We explain how it is possible to obtain the necessary conditions on functions defining a germ of planar web in order that it be of maximal rank. Then we apply this method to the study of maximal rank 5-webs. We show the existence of many exceptional 5-webs non-equivalent to Bol's web, thus giving an answer to Chern's problem. To cite this article: L. Pirio, C. R. Acad. Sci. Paris, Ser. I 339 (2004).




© 2004  Académie des sciences@@#104156@@

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