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July, 2006 A group-theoretic characterization of the space obtained by omitting the coordinate hyperplanes from the complex Euclidean space, II
Akio KODAMA, Satoru SHIMIZU
J. Math. Soc. Japan 58(3): 643-663 (July, 2006). DOI: 10.2969/jmsj/1156342031

Abstract

In this paper, we prove that the holomorphic automorphism groups of the spaces C k × ( C * ) n - k and ( C k - { 0 } ) × ( C * ) n - k are not isomorphic as topological groups. By making use of this fact, we establish the following characterization of the space C k × ( C * ) n - k : Let M be a connected complex manifold of dimension n that is holomorphically separable and admits a smooth envelope of holomorphy. Assume that the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of C k × ( C * ) n - k as topological groups. Then M itself is biholomorphically equivalent to C k × ( C * ) n - k . This was first proved by us in [5] under the stronger assumption that M is a Stein manifold.

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Akio KODAMA. Satoru SHIMIZU. "A group-theoretic characterization of the space obtained by omitting the coordinate hyperplanes from the complex Euclidean space, II." J. Math. Soc. Japan 58 (3) 643 - 663, July, 2006. https://doi.org/10.2969/jmsj/1156342031

Information

Published: July, 2006
First available in Project Euclid: 23 August 2006

zbMATH: 1099.32007
MathSciNet: MR2254404
Digital Object Identifier: 10.2969/jmsj/1156342031

Subjects:
Primary: 32M05
Secondary: 32Q28

Keywords: holomorphic automorphism groups , holomorphic equivalences , torus actions

Rights: Copyright © 2006 Mathematical Society of Japan

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Vol.58 • No. 3 • July, 2006
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