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Currently displaying 1 – 3 of 3

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Über die Methode der Polyederentwicklung der Kompakten und ihre Anwendungen auf die Abbildungstheorie

Makoto Abe — 1940

Compositio Mathematica

Holomorphic line bundles and divisors on a domain of a Stein manifold

Makoto Abe — 2007

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $D$ be an open set of a Stein manifold $X$ of dimension $n$ such that $H^{k} (D, 𝒪) = 0$ for $2 \leq k \leq n - 1$ . 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 $D$ .

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

Makoto Abe — 2004

Annales Polonici Mathematici

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 𝔡 on D.

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