Let be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form where is compact. Assume that the characteristic fiber of has the compact approximation property. Let be the complex dimension of and . Then: If is a holomorphic vector bundle (of finite rank) with , then . In particular, if , then .
@article{ASNSP_2007_5_6_1_15_0, author = {Leiterer, J\"urgen}, title = {A finiteness theorem for holomorphic {Banach} bundles}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {15--37}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 6}, number = {1}, year = {2007}, mrnumber = {2341512}, zbl = {1178.32016}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2007_5_6_1_15_0/} }
TY - JOUR AU - Leiterer, Jürgen TI - A finiteness theorem for holomorphic Banach bundles JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 15 EP - 37 VL - 6 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2007_5_6_1_15_0/ LA - en ID - ASNSP_2007_5_6_1_15_0 ER -
%0 Journal Article %A Leiterer, Jürgen %T A finiteness theorem for holomorphic Banach bundles %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 15-37 %V 6 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2007_5_6_1_15_0/ %G en %F ASNSP_2007_5_6_1_15_0
Leiterer, Jürgen. A finiteness theorem for holomorphic Banach bundles. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, pp. 15-37. http://www.numdam.org/item/ASNSP_2007_5_6_1_15_0/
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