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Extension property of holomorphic maps and the structure of complex manifolds

Research Project

Project/Area Number 19540100
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionSophia University

Principal Investigator

KATO Masahide  Sophia University, 理工学部, 教授 (90062679)

Co-Investigator(Kenkyū-buntansha) YOKOYAMA Kazuo  上智大学, 理工学部, 准教授 (10053711)
辻 元  上智大学, 理工学部, 教授 (30172000)
田原 秀敏  上智大学, 理工学部, 教授 (60101028)
山田 紀美子  上智大学, 理工学部, 助教 (70384170)
藤川 英華  上智大学, 理工学部, 助教 (80433788)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords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
Research Abstract

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.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (8 results)

All 2007 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Remarks (2 results)

  • [Journal Article] On Blanchard Manifolds2007

    • Author(s)
      Kato, Masahide ; Komada, Kazuya
    • Journal Title

      Tokyo Journal of Mathematics 30

      Pages: 397-401

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Blanchard Manifolds2007

    • Author(s)
      Kato, Masahide
    • Journal Title

      Tokyo Journal of Mathematics 30

      Pages: 397-401

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of invariant planes in a complex projective 3-space under discrete projective transformation groups

    • Author(s)
      Kato, Masahide
    • Journal Title

      To appear in Tokyo Journal of Mathematics

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compact Quotients with Positive Algebraic Dimensions of Large Domains in a Complex Projective 3-space

    • Author(s)
      Kato, Masahide
    • Journal Title

      To appear in the Journal of Mathematical Society of Japan

    • NAID

      10027871183

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compact Quotients with Positive Algebraic Dimensions of Large Domains in a Complex Projective 3-space

    • Author(s)
      Kato, Masahide
    • Journal Title

      Journal of the Mathematical Society of Japan (To appear(確定))

    • NAID

      10027871183

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of invariant planes in a complex projective 3-space under discrete projective transformation groups

    • Author(s)
      Kato, Masahide
    • Journal Title

      Tokyo Journal of Mathematics (To appear(確定))

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Remarks]

    • URL

      http://www.mm.sophia.ac.jp/~kato/

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.mm.sophia.ac.jp/~kato/

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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