IJPAM: Volume 11, No. 4 (2004)

SUBSETS OF OPEN SUBSETS OF ${\bf {C}}^{({\bf {N}})}$

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

Abstract.Let $V$ be a closed analytic subset of an open subset of ${\bf {C}}^{({\bf {N}})}$ such that the intersection of $V$ with all finite-dimensional coordinate subspaces $L_n$ is cohomologically $q$-complete. Then $H^i(V,E)=0$ for every $i>q$ and every holomorphic vector bundle $E$ with finite rank on $V$. If $L_n\cap V$ is assumed to be smooth and $q$-complete for all $n>0$, then $H^i(V,E)=0$ for every $i>q$ even if $E$ has fibers isomorphic to a Banach space.

Received: January 8, 2004

AMS Subject Classification: 32K05, 32F10, 32L05, 32L10

Key Words and Phrases: infinite-dimensional complex space, $q$-complete complex space, cohomologically $q$-complete complex space, holomorphic Banach bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 11
Issue: 4