Holomorphic line bundles on a domain of a two-dimensional Stein manifold
Volume 83 / 2004
Annales Polonici Mathematici 83 (2004), 269-272
MSC: 32E10, 32L10, 32T05.
DOI: 10.4064/ap83-3-8
Abstract
Let $D$ be an open subset of a two-dimensional Stein manifold $S$. Then $D$ is Stein if and only if every holomorphic line bundle $L$ on $D$ is the line bundle associated to some (not necessarily effective) Cartier divisor $\mathfrak{d}$ on $D$.
