2000/04/11 by Jean-Pierre Demailly, Demailly, Jean-Pierre
Mathematics · #14B05 #14J45 #32C17 #32J25 #32S05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG #msc:14B05 #msc:14J45 #msc:32C17 #msc:32J25 #msc:32S05
paper · pdf · doi:10.48550/arxiv.math/0004067
5 pages, Plain-TeX (reason for resubmission: 2 references added)
openalex publication_date 2000/04/11 · arxiv created 2000/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.