A group-theoretic characterization of the space obtained by omitting the coordinate hyperplanes from the complex Euclidean space, II

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In this paper, we prove that the holomorphic automorphism groups of the spaces Ck × (C*)n-k and (Ck - {0}) × (C*)n-k are not isomorphic as topological groups. By making use of this fact, we establish the following characterization of the space Ck × (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 Ck × (C*)n-k as topological groups. Then M itself is biholomorphically equivalent to Ck × (C*)n-k. This was first proved by us in [5] under the stronger assumption that M is a Stein manifold.全文公開200907
日本数学会 = Mathematical Society of Japanの論文
2006-07-01