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Teichmueller groupoids and monodromy in conformal field theory

Research Project

Project/Area Number 13640031
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) UEHARA Tsuyoshi  Saga University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (80093970)
MITOMA taru  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)
HIROSE Susumu  Saga University, Faculty of Science and Engineering, Assistant Professor, 理工学部, 助教授 (10264144)
TEARAI Naoki  Saga University, Faculty of Science and Engineering, Assistant Professor, 文化教育学部, 助教授 (90259862)
田中 達治  佐賀大学, 理工学部, 教授 (80039370)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)
KeywordsConformal field theory / Teichmueller groupoids / Monodromy representation / Bogomolov conjecture / Abelian varieties / Neron-Tate height functions / hypergeometric equations / Riemann surfaces / 超幾何学方程式 / 代数曲線 / モジュライ空間 / ガロア表現 / アラケロフ幾何
Research Abstract

1. We described the monodromy representation of Teichmueller goupoids associated with conformal field theory. Extending Ullmo-Zhang's result on the Bogomolov conjecture, we gave a condition that a subvariety of an abelian variety is isomorphic to an abelian variety in terms of the value distribution of a Neron-Tate height function on the subvariety. We described the Riemann surfaces associated with the monodromy representation of hypergeometric equation with purely imaginary exponents.
2. We gave an explicit formula of the Hasse unit index for the unit group of quadratic fields, and considered a Problem of Hasse for the ring of integers in certain abelian fields.
3. We tried to justify the perturbative Chern-Simons theory using the asymptotic expansion theory via infinite dimensional stochastic analysis, and derived a simple Homfly polynomial.
4. We showed that for certain algebraic geometry codes, the minimum distance are equal to the Fang-Rao bound, and found an algebraic geometry code of other type with same property.
5. We gave the upper bound for the average number of connected components of the induced subgraphs of the graphs for simplicial polytopes, and proved that the arithmetical rank is equal to the projective dimension for the almost complete intersection Stanley-Reisner ideals.
6. We calculated the virtual cohomological dimension and the Euler number of the mapping class group of a three-dimensional handlebody.

Report

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

    (23 results)

All Other

All Publications (23 results)

  • [Publications] Takashi Ichikawa: "Teichmueller groupoids and Galois action"J.Reine Angew.Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Ichikawa, Masaaki Yoshida: "On Schottky groups arising from the hypergeometric equation with imaginary exponents"Proc.Amer.Math.Soc.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.I.A.Shah, Toru Nakahara: "Monogenesis of the rings of integers in certain imaginary abelian fields"Nagoya Math.J.. 168. 85-92 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Motoda, Toru Nakahara, S.I.A.Shah: "On a problem of Hasse for certain imaginary abelian fields"J.Number Theory. 96. 326-334 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Hyeong-Kee Song, Tsuyoshi Uehara: "On the Feng-Rao bound for the minimum distance of certain algebraic geometry codes"Kyushu J.Math.. 56. 405-418 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Susumu Hirose: "A complex of curves and of a presentation for the mapping class group of a surface"Osaka J.of Math.. 39. 795-820 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Ichikawa: "Teichmueller groupoids and Galois action"J. Reine Angew. Math.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Ichikawa and Masaaki Yoshida: "On Schottky groups arising from the hypergeometric equation with imaginary exponents"Proc. Amer. Math. Soc.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. I. A. Shah and T. Nakahara: "Monogenesis of the rings of integers in certain imaginary abelian fields"Nagoya Math. J.. Vol.168. 85-92 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Motoda, T. Nakahara, S. I. A. Shah: "On a Problem of Hasse for certain imaginary abelian fields"J. Number Theory. Vol.96. 326-334 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Hyeong-Kee Song and Tsuyoshi Uehara: "On the Feng-Rao bound for the minimum distance of certain algebraic geometry codes"Kyushu J. Math.. Vol.56. 405-418 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Susumu Hirose: "A complex of curves and a presentation for the mapping class group of a surface"Osaka J. of Math.. Vol.39. 795-820 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Ichikawa: "Teichmueller groupoids and Galois action"J. Reine Angew. Math.. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] Takashi Ichikawa, Masaaki Yoshida: "On Schottky groups arising from the hypergeometric equation with imaginary exponents"Proc. Amer. Math. Soc.. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] S.I.A.Shah, Toru Nakahara: "Monogenesis of the rings of integers in certain imaginary abelian fields"Nagoya Math. J.. 168. 85-92 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Matoda, Toru Nakahara, S.I.A.Shah: "On a problem of Hasse for certain imaginary abelian fields"J. Number Theory. 96. 326-334 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hyeong-Kee Song, Tsuyoshi Uehara: "On the Feng-Rao bound for the minimum distance of certain algebraic geometry codes"Kyushu J. Math.. 56. 405-418 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Susumu Hirose: "A Complex of curves and a presentation for the mapping class group of a surface"Osaka J. of Math.. 39. 795-820 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Takashi Ichikawa: "Universal periods of hyperelliptic curves and their applications"J.Pure Appl.Algebra. 163. 277-288 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Toru Nakahara et al.: "On the unit group and the class number of certain composita of two real quadratic fields"Manuscripta Math.. 105. 85-101 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Toru Nakahara, S.I.Shah: "Monogenesis of the rings of integers in certain imaginary abelian fields"Nagoya Math.J.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] H.-K.Song, Tsuyoshi Uehara: "On the Feng-Rao bound for the minimum distance of certain algebraic geometry codes"Kyushu J. of Math.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Susumu Hirose: "A complex of curves and a presentation for the mapping class group of a surface"Osaka J. of Math.. (to appear).

    • Related Report
      2001 Annual Research Report

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

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