Extension property of holomorphic maps and the structure of complex manifolds

全纯映射的可拓性与复流形的结构

• 批准号: 19540100
• 负责人: KATO Masahide
• 金额: $ 1.33万
• 依托单位: Sophia University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540100/
• 关键词: 幾何学; 複素多様体; 正則写像の拡張; non-Kaehler, Klein群; non-Kaehler; Klein群; Non-Kaehler; Klein群理論; pluri-closed metric

We are studying a method to get some information of the structure of a given complex manifold by measuring the extendibility of holomorphic maps of Hartogs domains to the given manifold. As an application of the method, we have obtained the following result. For a finitely generated three dimensional discrete projective transformation group Γ with some discontinuity condition, we can define canonically a non-singular quotient space X(Γ) of an open subset of a projective 3-space. We have shown that, if X(Γ) contains a compact connected component with positive algebraic dimension, then X(Γ) is connected, and that X(Γ) is biholomorphic to one of the three kinds of well-known 3-folds.

本文研究了一种通过度量Hartogs域上的全纯映射到给定复流形上的可扩性来获得复流形结构信息的方法。作为该方法的一个应用，我们得到了如下结果.对于一个具有不连续性条件的三维离散射影变换群Γ，我们可以定义一个射影空间的开子集的非奇异商空间X（Γ）.我们证明了，如果X（Γ）包含一个代数维数为正的紧连通分支，则X（Γ）是连通的，并且X（Γ）是双全纯的三种著名的3-折叠之一.

项目成果

On Blanchard Manifolds

关于布兰查德流形

• 发表时间: 2007
• 期刊: Tokyo Journal of Mathematics 30
• 作者: Kato;Masahide ; Komada;Kazuya
• 通讯作者: Kazuya

Existence of invariant planes in a complex projective 3-space under discrete projective transformation groups

离散射影变换群下复射影三空间中不变平面的存在性

• 期刊: To appear in Tokyo Journal of Mathematics
• 作者: Kato;Masahide
• 通讯作者: Masahide

Compact Quotients with Positive Algebraic Dimensions of Large Domains in a Complex Projective 3-space

复射影3空间中大域的正代数维数紧商

• 期刊: To appear in the Journal of Mathematical Society of Japan
• 作者: Kato;Masahide
• 通讯作者: Masahide