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Dualite pour les feuilletages transversalement holomorphes

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Abstract

Let F be a transversely holomorphic codimension n foliation on a compact orientable manifold M and E a foliated holomorphic vector bundle on M. We prove that the cohomology

of M with coefficients in the sheaf

of E-valued holomorphic base-like differential forms satisfies Serre duality. Some computations are given. In case n=1 we show that the base-like cohomology H*(M/F,ℂ) is finite dimensional.

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Authors and Affiliations

  1. U.F.R. de Mathématiques, Université de Lille I U.A. au C.N.R. 751, 59655, Villeneuve d'Ascq Cedex, France

    Aziz El Kacimi Alaoui

  2. U.F.R. de Mathématiques et Sciences Economiques, Université de Lille III, 59653, Villeneuve d'Ascq Cedex, France

    Aziz El Kacimi Alaoui

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  1. Aziz El Kacimi Alaoui
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Kacimi Alaoui, A.E. Dualite pour les feuilletages transversalement holomorphes. Manuscripta Math 58, 417–443 (1987). https://doi.org/10.1007/BF01277603

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  • DOI: https://doi.org/10.1007/BF01277603

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