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.

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
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     title = {Holomorphic line bundles and divisors on a domain of a {Stein} manifold},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
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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. http://archive.numdam.org/item/ASNSP_2007_5_6_2_323_0/

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