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

Makoto Abe

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

  • Volume: 6, Issue: 2, page 323-330
  • ISSN: 0391-173X

Abstract

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Let D be an open set of a Stein manifold X of dimension n such that H k ( D , 𝒪 ) = 0 for 2 ≤ k ≤ 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 .

How to cite

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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 6.2 (2007): 323-330. <http://eudml.org/doc/272258>.

@article{Abe2007,
abstract = {Let $D$ be an open set of a Stein manifold $X$ of dimension $n$ such that $H^\{k\}(D, \mathcal \{O\}) = 0$ for $2 \le k \le n - 1$. 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 $\mathfrak \{d\}$ on $D$.},
author = {Abe, Makoto},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {323-330},
publisher = {Scuola Normale Superiore, Pisa},
title = {Holomorphic line bundles and divisors on a domain of a Stein manifold},
url = {http://eudml.org/doc/272258},
volume = {6},
year = {2007},
}

TY - JOUR
AU - Abe, Makoto
TI - Holomorphic line bundles and divisors on a domain of a Stein manifold
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2007
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 2
SP - 323
EP - 330
AB - Let $D$ be an open set of a Stein manifold $X$ of dimension $n$ such that $H^{k}(D, \mathcal {O}) = 0$ for $2 \le k \le n - 1$. 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 $\mathfrak {d}$ on $D$.
LA - eng
UR - http://eudml.org/doc/272258
ER -

References

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