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On the Frobenius Integrability of Certain Holomorphic p-Forms

In: Complex Geometry

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  • Jean-Pierre Demailly

    (Université de Grenoble I, Département de Mathématiques, Institut Fourier)

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 semi-negative curvature on a compact Kähler manifold. There are in fact very strong restrictions, both on the holomorphic form and on the curvature of the semi-negative line bundle. In particular, 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.

Suggested Citation

  • Jean-Pierre Demailly, 2002. "On the Frobenius Integrability of Certain Holomorphic p-Forms," Springer Books, in: Ingrid Bauer & Fabrizio Catanese & Thomas Peternell & Yujiro Kawamata & Yum-Tong Siu (ed.), Complex Geometry, pages 93-98, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56202-0_6
    DOI: 10.1007/978-3-642-56202-0_6
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