Steinness of bundles with fiber a Reinhardt bounded domain

2004/08/20 by Karl Oeljeklaus, Oeljeklaus, Karl, Dan Zaffran +1
Mathematics · #32A07 #32E10 #32L05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32A07 #msc:32E10 #msc:32L05

paper · pdf · doi:10.48550/arxiv.math/0408284

To appear in Bull. Soc. Math. France

arxiv created 2006/02/03 · arxiv updated 2009/12/01

Abstract

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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