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Comptes Rendus Mathématique
Volume 343, n° 7
pages 479-482 (octobre 2006)
Doi : 10.1016/j.crma.2006.09.006
Received : 26 April 2006 ;  accepted : 5 September 2006
Surfeuilletages de feuilletages holomorphes singuliers non dégénérés en dimension 2 et 3
Overfoliations of non-degenerate singular holomorphic foliations in dimension 2 and 3
 

Ludovic Landuré
LAREMA, Université dʼAngers, 2, boulevard Lavoisier, 49045 Angers cedex 01, France 

Résumé

Nous étudions des feuilletages Levi-plats dont la partie complexe est un feuilletage holomorphe ayant une singularité isolée en lʼorigine de   ou de  . En dimension 2, nous montrons que, si la partie complexe est non dégénérée ou non dégénérée après un éclatement, alors le feuilletage Levi-plat et sa partie complexe sont chacun décrits par une intégrale première submersive sauf en lʼorigine. En dimension 3, nous montrons quʼun champ de vecteurs linéaire nʼest jamais la partie complexe dʼun feuilletage Levi-plat de codimension 3. Pour citer cet article : L. Landuré, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Abstract

We study Levi-flat foliations which complex part is an holomorphic foliation with an isolated singularity at the origin of   or  . In dimension 2, we show that, if the complex part is non-degenerate or non-degenerate after one blow up, then the Levi-flat foliation and its complex part are both described by a first integral which is submersive on  . In dimension 3, we show that a linear vector field is never the complex part of a codimension 3 Levi-flat foliation. To cite this article: L. Landuré, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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