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Motivic aspect of moduli space of algebraic curves

Research Project

Project/Area Number 11640035
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionSaga University

Principal Investigator

ICHIKAWA Takashi  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (20201923)

Co-Investigator(Kenkyū-buntansha) MITOMA Itaru  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (40112289)
NAKAHARA Toru  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (50039278)
TANAKA Tatsuji  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (80039370)
HIROSE Susumu  Saga University, Faculty of Science and Engineering, Lecturer, 理工学部, 講師 (10264144)
UEHARA Tsuyoshi  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (80093970)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2000: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1999: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsTeichmueller groupoid / Moduli space / Riemann surface / Algebraic curve / Uniformization / Galois representation / Monodromy representation / Mapping class group / ガロア作用 / チャーン・サイモンズ積分 / 代数幾何符号
Research Abstract

1. Teichmueller groupoids are fundamental groupoids of the moduli space of pointed Riemann surfaces, and are studied in topology and mathematical physics. Using the arithmetic Schottky-Mumford uniformization theory on algebraic curves given by the head investigator, we constructed Teichmueller groupoids in the category of arithmetic geometry.
2. Using the result in 1, we verified Grothendieck's conjecture on motives attached to Teichmueller groupoids for Galois representations and monodromy representations given by conformal field theory, i.e. showed that these objects are generated by basic ones.
3. We described explicitly the Chow-forms of elliptic normal curves of degree 4, and showed that certain projective algebraic varieties admit Chow-forms having a special property.
4. We studied unit groups, class numbers and integer rings for some abelian number fields.
5. We discussed the infinite level asymptotics of the perturbative Chern-Simons integral without renormalization, by introducing a Gaussian kernel increasing along the level tends to infinity.
6. We determined the minimum distances of evaluation codes of the Hermite type, and constructed the bases of a part of trace-norm codes.
7. Using complex of curves, we obtained Gervais' symmetric presentation for the mapping class group of a surface. Furthermore, we determined the virtual cohomological dimension and the Euler number of the mapping class group of a 3-dimensional handlebody.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] Takashi Ichikawa: "Generalized Tate curve and integral Teichmuller modular forms"Amer.J.Math.. 122. 1139-1174 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Takashi Ichikawa: "Universal periods of hyperelliptic curves and their applications"J.Pure Appl.Algebra, to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Tatsuji Tanaka: "On the Chow-forms of elliptic normal curves of degree 4"Tsukuba J.Math.. 24. 109-125 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Toru Nakahara et al.: "On the units and the class number of certain composita of two quadratic fields"proc.Japan Acad.. 75A. 63-66 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Toru Nakahara et al.: "On arithmetic properties of generalized Fibonacci sequences"Rep.Fac.Sci.Engrg.Saga Univ.Math.. 28-1. 1-17 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Toru Nakahara et al.: "On the unit group and the class number of cetain composita of two real quadratic fields"Manuscripta Math.,. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Itaru Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Proc.Canad.Math.Soc.,. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Itaru Mitoma: "Infinite level asymptotics of a perturbative Chern-Simons integral"Stochastics in Finite and Infinite Dimensions,. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Tsuyoshi Uehara: "On minimum distance of algebraic-geometric codes"Adv.Stud.Contemp.Math.(Pusan). 1. 1-15 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Takashi Ichikawa: "Generalized Tate curve and integral Teichmueller modular forms"Amer.J.Math.. vol.122. 1139-1174 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Takashi Ichikawa: "Universal periods of hyperelliptic curves and their applications"J.Pure Appl.Algebra. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Tatsuji Tanaka: "On the Chow-forms of elliptic normal curves of degree 4"Tsukuba J.Math.. vol.24. 109-125 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Toru Nakahara et al.: "On the units and the class number of certain composita of two quadratic fields"Proc.Japan Acad.. vol.75 A. 63-66 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Toru Nakahara et al.: "On arithmetic properties of generalized Fibonacci sequences"Rep.Fac.Sci.Engrg.Saga Univ.Math.. vol.28-1. 1-17 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Toru Nakahara et al.: "On the unit group and the class number of cetain composita of two real quadratic fields"Manuscripta Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Itaru Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Proc.Canad.Math.Soc.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Itaru Mitoma: "Infinite level asymptotics of a perturbative Chern-Simons integral"Stochastics in Finite and Infinite Dimensions. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Tsuyoshi Uehara: "On minimun distance of algebraic-geometric codes"Adv.Stud.Contemp.Math.(Pusan). vol.1. 1-15 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Takashi Ichikawa: "Generalized Tate curve and integral Teichmuller modular forms"Amer.J.Math.. 122. 1139-1174 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Takashi Ichikawa: "Universal periods of hyperelliptic curves and their applications"J.Pure Appl.Algebra,. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Tatsuji Tanaka: "On the Chow-forms of elliptic normal curves of degree 4"Tsukuba J.Math.. 24. 109-125 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Toru Nakahara et al.: "On the unit group and the class number of cetain composita of two real quadratic fields"Manuscripta Math.,. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Itaru Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Proc.Canad.Math.Soc.,. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Itaru Mitoma: "Infinite level asymptotics of a perturbative Chern-Simons integral"Stochastics in Finite and Infinite Dimensions,. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Tatsuji Tanaka: "On the Chow-forms of elliptic normal curves of degree 4"Tsukuba Journal of Mathematics. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Toru Nakahara et al.: "On the units and the class numbers of certain composita of two guadratic tields"Proc.Japan Acad.,Ser.A. 75・4. 63-66 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Itaru Mitoma: "Wiener space approach to a perturbative Chern-Simons integral"Stochastic Processes,Physics and Geometry,New Interplays,Proceedings. (to appear).

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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