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Extension property of holomorphic maps and complex structures of the target manifolds

Research Project

Project/Area Number 17540094
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 Univ., Faculty of Science and Tech., Professor, 理工学部, 教授 (90062679)

Co-Investigator(Kenkyū-buntansha) TSUJI Hajime  Sophia Univ., Faculty of Science and Tech., Professor, 理工学部, 教授 (30172000)
TAHARA Hidetoshi  Sophia Univ., Faculty of Science and Tech., Professor, 理工学部, 教授 (60101028)
YOKOYAMA Kazuo  Sophia Univ., Faculty of Science and Tech., Associate Professor, 理工学部, 助教授 (10053711)
AOYAGI Miki  Tokyo Institute of Technology, Precision and intelligence Lab., Researcher, 精密工学研究所, 研究員 (90338434)
YAMADA Mikiko  Sophia Univ., Faculty of Science and Tech., Assistant, 理工学部, 助手 (70384170)
谷口 肇  上智大学, 理工学部, 助教授 (40053657)
Project Period (FY) 2005 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
KeywordsExtension of holomorphic map / Klein group / Complex projective structure / non-Kaehler / 複素多様体 / Harotgs現象 / Schwarz微分方程式
Research Abstract

1.We defined in our previous work an index which measures the extendibility of holomorphic maps of a Hartogs domain to complex manifolds. This index is useful to study quotient manifolds of "large" domains in complex projective 3-spaces. Here a domain in projective 3-space P^3 is "large", if the domain contains projective lines. Main result in this direction is the characterization of compact quotient of large domains with positive algebraic dimension. In this case, the large domain is dense in P^3 and the compement is very thin. Under an additional assumption, we could show that the quotient manifold is a P^3, a Blanchard manifold, or a L-Hopf manifold. We think that this additional assumption can be removed soon. To obtain this result we use also a recent result of S.Ivashkovich on extension of holomorphic maps into non-Kaehler manifolds.
2.The result above is an analogy of the elementary type group case in Klein group theory of complex 1-dimension and suggests a possibility of constructing higher dimensional complex analytic Klein group theory. We could give basic definitions to develop 3-dimensional complex analytic Klein group theory and formulate many problems.
3.Our research plan in the early stage was to seek good sufficient conditions of complex manifolds to be "probable". At present we have no results in this direction.

Report

(3 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • Research Products

    (13 results)

All 2006 2005

All Journal Article (13 results)

  • [Journal Article] Compact quotients of large domains in a complex projective 3-spaces2006

    • Author(s)
      Masahide Kato
    • Journal Title

      Tokyo Journal of Mathematics 29.1

      Pages: 209-232

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Compact quotients of large domains in a complex projective 3-space2006

    • Author(s)
      Masahide Kato
    • Journal Title

      Tokyo J.Math. 29

      Pages: 209-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Compact quotients of large domains in a complex projective 3-space2006

    • Author(s)
      Masahide Kato
    • Journal Title

      Tokyo Journal of Mathematics 29.1

      Pages: 209-232

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Uniqueness of the solution of nonlinear totally characteristic partial differential equations2005

    • Author(s)
      Hidetoshi Tahara
    • Journal Title

      Journal of Mathematical Society of Japan 57

      Pages: 1045-1065

    • NAID

      10017178079

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Structure of solutions of nonlinear partial differential equations of Gerard-Tahara type2005

    • Author(s)
      Hidetoshi Tahara
    • Journal Title

      Publ. Res. Inst. Math. Sci. 41

      Pages: 339-373

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stochastic Complexities of Reduced Rank Regression in Bayesian Estimation2005

    • Author(s)
      Miki Aoyagi
    • Journal Title

      Neural Networks 18

      Pages: 924-933

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Uniqueness of the solution of nonlinear totally characteristic partial differential equations2005

    • Author(s)
      Hidetoshi Tahara
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 1045-1065

    • NAID

      10017178079

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Structure of solutions of nonlinear partial differential equations of Gerard-Tahara type2005

    • Author(s)
      Hidetoshi Tahara
    • Journal Title

      Publ.Res.Inst.Math.Sci. 41

      Pages: 339-373

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stochastic complexities of reduced rank regression in Bayesian estimation2005

    • Author(s)
      Miki Aoyagi
    • Journal Title

      Neural Networks 18

      Pages: 924-933

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Uniqueness of the solution of nonlinear totally characteristic partial differential equations2005

    • Author(s)
      H.Tahara
    • Journal Title

      J.Math.Soc.Japan 57

      Pages: 1045-1065

    • NAID

      10017178079

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Structure of solutions of nonlinear partial differential equations of Gerard-Tahara type.2005

    • Author(s)
      H.Tahara
    • Journal Title

      Publ.Res.Inst.Math.Sci. 41

      Pages: 339-373

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Stochastic Complexities of Reduced Rank Regression in Bayesian Estimation2005

    • Author(s)
      M.Aoyagi
    • Journal Title

      Neural Networks. 18

      Pages: 924-933

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 特異点解消とニューラルネットワークのベイズ推定における汎化誤差2005

    • Author(s)
      M.Aoyagi
    • Journal Title

      電子情報通信学会和文論文誌 J88-D-II, 10

      Pages: 2112-2124

    • NAID

      110003224123

    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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