Let be an open set of a Stein manifold of dimension such that for . We prove that is Stein if and only if every topologically trivial holomorphic line bundle on is associated to some Cartier divisor on .
@article{ASNSP_2007_5_6_2_323_0,
author = {Abe, Makoto},
title = {Holomorphic line bundles and divisors on a domain of a {Stein} manifold},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {323--330},
year = {2007},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {2},
mrnumber = {2352521},
zbl = {1142.32007},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2007_5_6_2_323_0/}
}
TY - JOUR AU - Abe, Makoto TI - Holomorphic line bundles and divisors on a domain of a Stein manifold JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 323 EP - 330 VL - 6 IS - 2 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2007_5_6_2_323_0/ LA - en ID - ASNSP_2007_5_6_2_323_0 ER -
%0 Journal Article %A Abe, Makoto %T Holomorphic line bundles and divisors on a domain of a Stein manifold %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 323-330 %V 6 %N 2 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2007_5_6_2_323_0/ %G en %F ASNSP_2007_5_6_2_323_0
Abe, Makoto. Holomorphic line bundles and divisors on a domain of a Stein manifold. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 2, pp. 323-330. https://www.numdam.org/item/ASNSP_2007_5_6_2_323_0/
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