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On the Frobenius integrability of certain holomorphic p-forms

Jean-Pierre Demailly
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Abstract

The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with seminegative curvature on a compact Kaehler manifold. There are in fact very strong restrictions, both on the holomorphic form and on the curvature of the seminegative line bundle. As a consequence, these observations provide interesting information on the structure of projective manifolds which admit a contact structure: either they are Fano manifolds or, thanks to results of Kebekus-Peternell-Sommese-Wisniewski, they are biholomorphic to the projectivization of the cotangent bundle of another suitable projective manifold.

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Jean-Pierre Demailly. 2000-05-01. On the Frobenius integrability of certain holomorphic p-forms. https://arxiv.org/abs/math/0004067

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