Holomorphic line bundles on a domain of a two-dimensional Stein manifold

Volume 83 / 2004

Makoto Abe Annales Polonici Mathematici 83 (2004), 269-272 MSC: 32E10, 32L10, 32T05. DOI: 10.4064/ap83-3-8


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 $D$.


  • Makoto AbeSchool of Health Sciences
    Kumamoto University
    Kumamoto 862-0976, Japan

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