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

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

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 58(3), 643-663, 2006-07-01 

    日本数学会 = Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10018381026
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    7987055
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  IR  J-STAGE 
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