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Steinness of bundles with fiber a Reinhardt bounded domain

Karl Oeljeklaus; Dan Zaffran

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 4, page 451-473
  • ISSN: 0037-9484

Abstract

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Let E denote a holomorphic bundle with fiber D and with basis B . Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3 , we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1 ); for d = 2 , we give necessary and sufficient criteria for E to be Stein (Theorem 2 ). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem 3 ).

How to cite

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Oeljeklaus, Karl, and Zaffran, Dan. "Steinness of bundles with fiber a Reinhardt bounded domain." Bulletin de la Société Mathématique de France 134.4 (2006): 451-473. <http://eudml.org/doc/272463>.

@article{Oeljeklaus2006,
abstract = {Let $E$ denote a holomorphic bundle with fiber $D$ and with basis $B$. Both $D$ and $B$ are assumed to be Stein. For $D$ a Reinhardt bounded domain of dimension $d=2$ or $3$, we give a necessary and sufficient condition on $D$ for the existence of a non-Stein such $E$ (Theorem $1$); for $d=2$, we give necessary and sufficient criteria for $E$ to be Stein (Theorem $2$). For $D$ a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for $E$ to be Stein (Theorem $3$).},
author = {Oeljeklaus, Karl, Zaffran, Dan},
journal = {Bulletin de la Société Mathématique de France},
keywords = {holomorphic fiber bundle; Stein manifold; bounded Reinhardt domain; Serre problem},
language = {eng},
number = {4},
pages = {451-473},
publisher = {Société mathématique de France},
title = {Steinness of bundles with fiber a Reinhardt bounded domain},
url = {http://eudml.org/doc/272463},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Oeljeklaus, Karl
AU - Zaffran, Dan
TI - Steinness of bundles with fiber a Reinhardt bounded domain
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 4
SP - 451
EP - 473
AB - Let $E$ denote a holomorphic bundle with fiber $D$ and with basis $B$. Both $D$ and $B$ are assumed to be Stein. For $D$ a Reinhardt bounded domain of dimension $d=2$ or $3$, we give a necessary and sufficient condition on $D$ for the existence of a non-Stein such $E$ (Theorem $1$); for $d=2$, we give necessary and sufficient criteria for $E$ to be Stein (Theorem $2$). For $D$ a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for $E$ to be Stein (Theorem $3$).
LA - eng
KW - holomorphic fiber bundle; Stein manifold; bounded Reinhardt domain; Serre problem
UR - http://eudml.org/doc/272463
ER -

References

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