Un théorème du type d'Oka–Levi pour les domaines étalés au dessus de variétés projectives

✍ Scribed by Pascal Dingoyan

• Publisher: Elsevier Science
• Year: 1999
• Tongue: French
• Weight: 183 KB
• Volume: 123
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/s0007-4497(99)00002-0

✦ Synopsis

In this article, we study spread domains Π : U → V over a projective manifold V such that Π to be a Stein morphism, e.g., hull of meromorphy. We prove, such a domain is an existence domain of some holomorphic section s ∈ H 0 (U, E l ), where E = Π * (H ), H an ample line bundle on V . This is done by proving some line bundle convexity theorem for U . We deduce various results, e.g., a Lelong-Bremermann theorem for almost plurisubharmonic functions and a general Levi type theorem: Let U → V a locally pseudoconvex spread domain over a projective manifold, then U is an almost domain of meromorphy, that is Ũ \ U = H some hypersurface in Ũ , the hull of meromorphy of U . Hence, if W is a general spread domain over V then its pseudoconvex hull is obtained from its meromorphic hull minus some hypersurface.