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

Akio Kodama, Satoru Shimizu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)643-663
Number of pages21
JournalJournal of the Mathematical Society of Japan
Volume58
Issue number3
DOIs
Publication statusPublished - 2006 Jul

Keywords

  • Holomorphic automorphism groups
  • Holomorphic equivalences
  • Torus actions

ASJC Scopus subject areas

  • Mathematics(all)

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