Holomorphic line bundles and divisors on a domain of a Stein manifold
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 6 (2007) no. 2, p. 323-330
Let D be an open set of a Stein manifold X of dimension n such that H k (D,𝒪)=0 for 2kn-1. We prove that D is Stein if and only if every topologically trivial holomorphic line bundle L on D is associated to some Cartier divisor 𝔡 on D.
Classification:  32E10,  32L10,  32Q28
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {2},
     year = {2007},
     pages = {323-330},
     zbl = {1142.32007},
     mrnumber = {2352521},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 6 (2007) no. 2, pp. 323-330. http://www.numdam.org/item/ASNSP_2007_5_6_2_323_0/

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