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

Abstract

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 U ̃ \\U=H some hypersurface in U ̃ , 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.