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Pré-Publication, Document De Travail Année : 2004

Steinness of bundles with fiber a Reinhardt bounded domain

Dan Zaffran
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Résumé

Let E denote a 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 two or three: (1) We give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1); (2) We give a necessary and sufficient criterion 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).

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Dates et versions

hal-00002645 , version 1 (20-08-2004)
hal-00002645 , version 2 (20-08-2004)
hal-00002645 , version 3 (14-10-2004)
hal-00002645 , version 4 (12-02-2005)
hal-00002645 , version 5 (03-02-2006)

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Karl Oeljeklaus, Dan Zaffran. Steinness of bundles with fiber a Reinhardt bounded domain. 2004. ⟨hal-00002645v3⟩
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