Local transversely product singularities

Lins-Neto, Alcides

Annales Henri Lebesgue, Tome 4 (2021), pp. 485-502.

Nous démontrons qu’un feuilletage de codimension un de ${\mathbb{P}}^n$ qui est localement un produit autour de tous les points d’une composante de codimension $2$ de l’ensemble singulier, a une composante de Kupka. En particulier, nous obtenons une généralisation d’un résultat déjà connu de Calvo Andrade et Brunella sur les feuilletages avec une composante de Kupka.

In the main result of this paper we prove that a codimension one foliation of ${\mathbb{P}}^n$, which is locally a product near every point of some codimension two component of the singular set, has a Kupka component. In particular, we obtain a generalization of a known result of Calvo Andrade and Brunella about foliations with a Kupka component.

Classification : 37F75, 34M15
Mots clés : foliation, locally product

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