Steinness of bundles with fiber a Reinhardt bounded domain
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).
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- August 2004
- DOI:
- 10.48550/arXiv.math/0408284
- arXiv:
- arXiv:math/0408284
- Bibcode:
- 2004math......8284O
- Keywords:
-
- Mathematics - Complex Variables;
- 32E10;
- 32A07;
- 32L05
- E-Print:
- To appear in Bull. Soc. Math. France