IJPAM: Volume 1, No. 2 (2002)

HOLOMORPHIC VECTOR BUNDLES ON
OPEN SUBSETS OF STEIN MANIFOLDS

E. Ballico
Dept. of Mathematics
University of Trento
38050 Povo (TN), ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $Z$ be a connected complex Stein manifold and $X$ an open subset of $Z$ such that every holomorphic function on $X$ extends to a holomorphic function on $Z$. Assume $X \ne Z$. Here we prove the existence of non-trivial holomorphic vector bundles on $X$. If $Z$ is affine and $X$ is an algebraic Zariski open subset of $Z$ we prove the existence of algebraic vector bundles on $X$ which are not trivial as holomorphic vector bundles.

Received: January 22, 2002

AMS Subject Classification: 32L05, 32E10, 14F05, 14R99

Key Words and Phrases: holomorphic vector bundle, Stein manifold, quasi-affine variety, envelope of holomorphy

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 2