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Topology related to Valuation problems and Numerical Computations

Research Project

Project/Area Number 13640067
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionThe University of Electro-Communications

Principal Investigator

YAMAGUCHI Kohei  Univ.Electro-Commun., Fac.of Elector-Commun., Professor, 電気通信学部, 教授 (00175655)

Co-Investigator(Kenkyū-buntansha) OHNO Masahiro  Univ.Electro-Commun., Fac.of Elector-Commun., Asso.Prof., 電気通信学部, 助教授 (70277820)
KIDA Masanari  Univ.Electro-Commun., Fac.of Elector-Commun., Asso.Prof., 電気通信学部, 助教授 (20272057)
NAITO Toshiki  Univ.Electro-Commun., Fac.of Elector-Commun., Professor, 電気通信学部, 教授 (60004446)
ISHIDA Haruhisa  Univ.Electro-Commun., Fac.of Elector-Commun., Lecturer, 電気通信学部, 講師 (80312792)
YAMADA Yuichi  Univ.Electro-Commun., Fac.of Elector-Commun., Lecturer, 電気通信学部, 講師 (30303019)
安藤 清  電気通信大学, 電気通信学部, 教授 (20096944)
田吉 隆夫  電気通信大学, 電気通信学部, 教授 (60017382)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordsprojective variety / Riemann surface / energy functional / configuration space / harmonic map / elliptic curve / algebraic torus / asymptic stability / リーマン画 / ラベル付き粒子の配置空間 / ラグラジアン / ホモトピー型 / 正則写像 / 曲面結び目 / labelled configuration space / 射影空間 / モース理論的原理 / universal covering / だ円曲線 / 高次分岐群
Research Abstract

Consider the energy functionals E on spaces consisting of all smooth maps from a Riemann surface to complex projective spaces. In this case, it is very important to study the spaces consisting of all critical points of E.K.Yamaguchi suceeds to define a finite dimensional homotopy configuration space models from a Riemann surface of genus g into a complex projective space for g>O. He also obtains a similar result for the space of algebraic maps between real projective spaces. Moreover, he shows that a homotopy asymptic stability theorem holds for such spaces of algebraic maps. Kida studies elliptic curves and algebraic field extensions associated to certain maps on algebraic torus. As an application he obtains an easy method for checking prime numbers. M.Ohno studied the vector bundles over non-singular projective varieties and investigated them from the point of view of "nef value". Y.Yamada studied the topology of 4-manifolds and obtained several results related to Gluck surgery.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] Y.Ono, K.Yamaguchi: "Group actions on spaces of rational functions"Publ.Res.Inst.Math.Soc.. 39-1. 173-181 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Koziowski, K.Yamaguchi: "Spaces of holomorphic maps between complex projective spaces of degree one"Topology and its Applications. 132-2. 139-145 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "Configuration space models for spaces of maps from a Riemann surface to complex projective space"Publ.Res.Inst.Math.. 39-3. 535-543 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "The topology of spaces of maps between real projective spaces"J.Math.Kyoto Univ.. 43-4(印刷中). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "Connective coverings of spaces of holomorphic maps"Osaka J.Math.. 40-3. 741-750 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "Mod p truncated configuration spaces"J.Math.Soc.Japan. 56-1. 193-199 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Ono, K.Yamaguchi: "Group actions on spaces of rational functions"Publ.Res.Inst.Math.Soc.. 39-1. 173-181 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] A.Kozlowski, K.Yamaguchi: "Spaces of holomorphic maps between complex projective spaces of degree one"Topology and its Appli.. 132-2. 139-145 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "Configuration space models for spaces of maps from a Riemann surface to complex projective space"Publ.Res.Inst.Math.Soc.. 39-3. 535-543 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "The topology of spaces of maps between real projective spaces"J.Math.Kyoto Univ.. 43-4(to appear). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "Connective coverings of spaces of holomorphic maps"Osaka J.Math.. 40-3. 741-750 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yamaguchi: "Mod p truncated configuration spaces"J.Math.Soc.Japan. 56-1(to appear). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Ono, K.Yamaguchi: "Group actions on spaces of rational functions"Publ.Res.Inst.Math.Soc.. 39-1. 173-181 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Kozlowski, K.Yamaguchi: "Spaces of holomorphic maps between complex projective spaces of degree one"Topology and Its Applications. 132-2. 139-145 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yamaguchi: "Configuration space models for spaces of maps from a Riemann surface to complex projective space"Publ.Res.Inst.Math.. 39-3. 535-543 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yamaguchi: "The topology of spaces of maps between real projective spaces"J.Math.Kyoto Univ.. 43-4(印刷中). (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yamaguchi: "Connective coverings of spaces of holomorphic maps"Osaka J.Math.. 40-3. 741-750 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yamaguchi: "Mod p truncated configuration spaces"J.Math.Soc.Japan. 56-1. 193-199 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yamaguchi: "Spaces of polynomials with real roots of bounded multiplicity"J. Math. Kyoto Univ.. 42-1. 105-115 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Yamaguchi: "Universal coverings of spaces of holomorphic maps"Kyushu J. Math.. 56-2. 381-389 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Hirata, K.Yamaguchi: "Spaces of polynomials without 3-fold real root"J. Math. Kyoto Univ.. 42-3(to appear). (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Ono, K.Yamaguchi: "Group actions on spaces of rational functions"Publ. R. I. M. S. Kyoto Univ.. 39-1. 173-181 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Yamaguchi: "Configuration space models for maps from a Riemann surface to complex projective space"Publ. R. I. M. S. Kyoto Univ.. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Yamaguchi: "Connective coverings of spaces of holomorphic maps"Osaka J. Math.. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Kohhei Yamaguchi: "Spaces of holomorphic maps with bounded multiplicity"Quart. J. Math.. 52. 249-259 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kohhei Yamaguchi: "Spaces of polynomials with reaI roots of bounded multiplicity"J. Math. Kyoto Univ.. (to appaear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Koichi Hirata, Kohhei Yamaguchi: "Spaces of polynomials without 3-fold real roots"J. Math. Kyoto Univ.. (to appaear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Kohhei Yamaguchi: "Universal coverings of spaces of holomorphic maps"Kyushu J. Math.. 56(to appaear). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Masanari Kida: "Nonexistence of elliptic curves having good reduction everywhere over Certain quadratic fields"Archiv. Math. (Besel). 76. 436-440 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Masanari Kida: "Good reduction of elliptic curves over imaginary quadratic filesdst"J. de Theorie de Nombres de Bordeaux. 13. 201-209 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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