IJPAM: Volume 11, No. 4 (2004)

COHOMOLOGICALLY -COMPLETE ANALYTIC
SUBSETS OF OPEN SUBSETS OF

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

Abstract.Let be a closed analytic subset of an open subset of such that the intersection of with all finite-dimensional coordinate subspaces is cohomologically -complete. Then for every and every holomorphic vector bundle with finite rank on . If is assumed to be smooth and -complete for all , then for every even if has fibers isomorphic to a Banach space.