IJPAM: Volume 16, No. 2 (2004)

HOLOMORPHIC VECTOR BUNDLES
AND PROPER HOLOMORPHIC MAPS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Here we explore the following definition. Let $f: X \to Z$ be a proper holomorphic map between reduced complex spaces such that $f_\ast (\mathcal {O}_X) = \mathcal {O}_Z$ and $E$ a holomorphic vector bundle on $X$. We will say that $E$ is new for $f$ if there is no holomorphic vector bundle $F$ on $Z$ such that $f^\ast (F) \cong \mathcal {O}_Z$. We give a few cases in which there are holomorphic vector bundles on $X$ with low rank and new for $f$. If $f$ is projective, we even show the existence of topologically trivial vector bundles which are new for $f$.

Received: June 11, 2004

AMS Subject Classification: 32L05, 32E05, 32F10

Key Words and Phrases: holomorphic vector bundle, holomorphically convex complex manifold, Stein space, proper holomorphic map

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 2