Steinness of bundles with fiber a Reinhardt bounded domain

Details Steinness of bundles with fiber a Reinhardt bounded domain Steinness of bundles with fiber a Reinhardt bounded domain

2004-08-20

arxiv.org/abs/math/0408284v5

Mathematics

Complex Variables

To appear in Bull. Soc. Math. France

Scientific paper

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 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).

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