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1998 Fiscal Year Final Research Report Summary

Study of Hyperplane Arrangements

Research Project

Project/Area Number 09440001
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTOKYO METROPOLITAN UNIVERSITY (1998)
Hokkaido University (1997)

Principal Investigator

TAKEDA Yuichiro  Tokyo Metropolitan University, Graduate School of Sciences, Assistant, 大学院・理学研究科, 助手 (30264584)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Hiroaki  Tokyo Metropolitan University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (60217883)
KURANO Kazuhiko  Tokyo Metropolitan University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (90205188)
URABE Tohsuke  Tokyo Metropolitan University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (70145655)
NAKAMURA Ken  Tokyo Metropolitan University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (80110849)
OKA Mutsuo  Tokyo Metropolitan University, Graduate School of Sciences, professor, 大学院・理学研究科, 教授 (40011697)
Project Period (FY) 1997 – 1998
Keywordshyperplane arrangement / hypergeometric integral / local system cohomology / reflection group
Research Abstract

(1)The following result was obtained concerning hyperplane arrangements which are naturally determined by reflection groups : the modules of vector fields which are doubly tangent to the hyperplane arrangements have free bases (Solomon Terao). This result is related to an actively-studied conjective by Richard Stanley about the * arrangements. The explicit bases have been successfully described. The description is deeply related with the Saito derivation.
(2)The families of combinationally-equivalent hyperplane arrangements can degonerate in many ways. It was proved that the corresponding Gauss-Marin connections have logarithric poles. This result has been expected by specialists, but has never ben proved for arbitrary combinationally-equivalent hyperplane arrangements.
(3)The loganithmic forms with poles along reflection arrangements have been characterized by using antiinvariant differential forms (Sheplen-Terao).

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] 寺尾宏明: "Bnbc-bases for local system cohomology on hyperplane complements" Transactions AMS. 349. 189-202 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 寺尾宏明: "The determinant of a hypergeometric period matrix" Inventiones Math.128. 417-436 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 寺尾宏明: "Twisted de Rham cohomology groups of logarithmic forms" Advances in Math.128. 119-152 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 寺尾宏明: "The double Coxeter arrangements" Commentarii Math. Helv.73. 237-258 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 寺尾宏明: "「超平面配置と超幾何積分」" 代数幾何城崎シンポジウム記録. 1-9 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 竹田雄一郎: "A relation between standard conjectnes and their arithmetric analogues" Kodai Math. J.(印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 石川剛郎,泉屋周一: "応用特異点論" 共立出版, (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中居功: "Web geometry and the equivalence problem of 1st order partial differential equations" フランス数学会, (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Terao, H.: "betanbc-bases for local system cohomology on hyperplane complements" Tramsactions AMS. 349. 189-202 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Terao, H.: "The determinant of a hypergeometric period matrix" Inventiones math.128. 417-436 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Terao, H.: "Twisted de Rham Cohomology groups of logarithmic forms" Advances in math. 128. 119-152 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Terao, H.: "The double Coxeter arrangements" Commentarii Math.Helv.73. 237-258 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Terao, H.: "Hyperplane arrangements and hypoergeometric integrals (in Japanese)" Proceedings of Kinosaki Symposium on Algebraic Geometry. 1-9 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takeda, Y.: "A relation between standard conjectures and their arithmetric analogues" Kodai Math.J.(in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ishikawa, G.-Izumiya, S.: Applied Singularity Theory (in Japanese). Kyoritsu Shuppan, (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nakai, I.: Web geometry and the equivalence problem of 1st order partial differential equations. French Math.Soc., (1998)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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