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Foliations with a Kupka component on algebraic manifolds. (English) Zbl 1058.32023

Summary: We consider codimension one holomorphic foliations in complex projective manifolds of dimension at least 3, having a compact Kupka component and represented by integrable holomorphic sections \(\omega\) of the bundle \(TM^*\otimes L\), where \(L\) denotes a very ample holomorphic line bundle. We show that, if the transversal type is not the radial vector field and \(H^1(M,\mathbb C)= 0\), then the foliation has a meromorphic first integral.

MSC:

32S65 Singularities of holomorphic vector fields and foliations
57R30 Foliations in differential topology; geometric theory
Full Text: DOI

References:

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