an:01331663
Zbl 0947.32010
Dingoyan, Pascal
A theorem of Oka-Levi type for étale domains over projective manifolds
FR
Bull. Sci. Math. 123, No. 5, 385-411 (1999).
0007-4497
1999
j
32L10 32Q28
hull of meromorphy; Lelong-Bremermann theorem; almost plurisubharmonic functions; Levi type theorem; spread domain over a projective manifold
Summary: We study spread domains \(\Pi:U\to V\) over a projective manifold \(V\) such that \(\Pi\) is a Stein morphism, e.g., hull of meromorphy. We prove that such a domain is an existence domain of some holomorphic section \(s\in H^0(U,E^l)\), where \(E=\Pi^*(H)\), \(H\) 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 \(U\to V\) a locally pseudoconvex spread domain over a projective manifold, then \(U\) is an almost domain of meromorphy, that is \(\widetilde U\setminus U=H\) some hypersurface in \(\widetilde U\), 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.