Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, pp. 811-854.

It is a known fact that the space of codimension one holomorphic foliations with singularities with a given ‘normal bundle’ has a natural structure of an algebraic variety. The aim of this paper is to consider the problem of the description of its irreducible components. To do this, we are interested in the problem of the existence of an integral factor of a twisted integrable differential 1–form defined on a projective manifold. We are going to do a geometrical analysis of the codimension one foliation associated to this form. The essential point of this paper consists in understanding the role played by a positive condition on some object associated to the foliation.

Il est connu que l’espace des feuilletages holomorphes de codimension 1 dont les singularités ont un fibré normal donné a la structure d’une variété algébrique. Le but de cet article est de décrire ses composantes irréductibles. Pour ceci, nous nous intéressons au problème de l’existence d’un facteur intégral pour une 1-forme différentielle tordue sur une variété projective. Nous ferons une analyse géométrique du feuilletage de codimension 1 associé à cette forme. Le point essentiel de cet article consiste en la compréhension du rôle joué par une condition de positivité sur un objet associé au feuilletage.

DOI: 10.5802/afst.1225
Calvo-Andrade, O. 1

1 CIMAT: Ap. Postal 402, Guanajuato, 36000, Gto. México
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Calvo-Andrade, O. Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, pp. 811-854. doi : 10.5802/afst.1225. http://www.numdam.org/articles/10.5802/afst.1225/

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