Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles
type: Item
instance of: scholarly article
title: Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles
zbMATH Open document ID: 1032.32012
DOI: 10.1007/BF03322737
published in: Results in Mathematics
publication date: 2003-10-29T00:00:00Z
review text: Let \(V\) be a complex Banach space (of infinite dimension) and \(X\subset \mathbb P(V)\) the transversal union of linear subspaces which all have the same finite codimension. More precisely: \(V\) is supposed to be a localizing Banach space with an unconditional countable basis (For these technicalities, see Lempert's papers). The author shows that any holomorphic vector bundle \(E\) of finite rank on \(X\) satisfies \(H^1(X,E)=0\) and is the direct sum of line bundles of the form \({\mathcal O}_X(n)\). The proof is based on the analogous result for \(X=\mathbb P(V)\) which was shown by \textit{L. Lempert} [J. Am. Math. Soc. 11, 485-520 (1998; Zbl 0904.32014)].
reviewed by: Bernd Kreußler
Mathematics Subject Classification ID: 32K05
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 1997683
zbMATH Keywords: infinite dimensional complex spaces
zbMATH Keywords: infinite dimensional projective spaces
zbMATH Keywords: holomorphic vector bundle
zbMATH Keywords: splitting of vector bundle
author: E. Ballico
MaRDI profile type: Publication
cites work: Q4317713
cites work: The Dolbeault complex in infinite dimensions I
cites work: The Dolbeault complex in infinite dimensions. III: Sheaf cohomology in Banach spaces
cites work: Q5614140
cites work: On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties
cites work: VECTOR BUNDLES OF FINITE RANK OVER INFINITE VARIETIES
full work available at URL: https://doi.org/10.1007/bf03322737
OpenAlex ID: W2071066877
description: scientific article; zbMATH DE number 1997683