Local transversely product singularities

Lins-Neto, Alcides

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

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.

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.

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

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