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Research on Complex Analytic Geometry and Singularity Theory

Research Project

Project/Area Number 02452001
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionHokkaido University

Principal Investigator

SUWA Tatsuo  Hokkaido University, Faculty of Science Professor, 理学部, 教授 (40109418)

Co-Investigator(Kenkyū-buntansha) NAKAI Isao  Hokkaido University, Faculty of Science Lecturer, 理学部, 講師 (90207704)
TOSE Nobuyuki  Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (00183492)
ISHIKAWA GOO  Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (50176161)
IZUMIYA Shyuichi  Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (80127422)
SUZUKI Haruo  Hokkaido University, Faculty of Science Professor, 理学部, 教授 (80000735)
中村 郁  北海道大学, 理学部, 助教授 (50022687)
田中 昇  北海道大学, 理学部, 教授 (80025296)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥6,700,000 (Direct Cost: ¥6,700,000)
Fiscal Year 1991: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1990: ¥4,400,000 (Direct Cost: ¥4,400,000)
KeywordsComplex analytic geometry / Singularity theory / Singular foliation / Unfolding theory / Singular set / 特異点の留数 / 時異葉層構造 / 開析理論 / 解複体 / 特性多様体
Research Abstract

The head investigators and the investigators did research in Complex Analytic Geometry and Singularity Theory. Especially, on the research of the singularities of complex analytic foliations which was proposed in the research plans for this project, a survey article was written summarizing the results on the unfolding theory, the determinacy problem, the structure of the singular set and the invariants associated to it which have been obtained mainly by the head investigator. This was presented at the College on Singularity Theory held in Trieste, Italy during the summer of 1991. Also, as to the invariants associated to the singular set, the Baum-Bott residues and the newly found Lehmann residues are studied and the fundamental principle underlying the appearance of these invariants is clarified and some generalizations of them are considered. As to the application of the D-module theory, which was proposed in the previous year, the investigations of the characteristic variety and the … More local structure of the-solution complex of the D-module associated to a complex analytic singular foliation and their relation with the aforementioned invariants are continued.
Besides the collaboration of the above research, each of the investigators did research on his own subject as well and obtained many results on the-following subject :
Holonomy groupoids for generalized foliations and the Chern-Simons-Maslov classes for symplectic boundles (Suzuki), applications of the singularity theory to the theory of differential equations, especially study of systems of completely integrable first order differential equations (Izumiya), singularity which appear in the projective geometry of curves and the maslov classes of Lagrangian varieties (Ishikawa), the microlocal analysis and its applications, especially the Morse inequality for R-constructible sheaves (Tose), analytic group actions on the complex plane, especially the existence of the separatrix and the proof of the rigidity theorem (Nakai). Less

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Tatsuo Suwa: "Finite determinacy of analytic foliation germs without formal integrating factors" Proc.Amer.Math.Soc.112. 989-997 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Haruo Suzuki: "Chern-Simons-Maslov classes in some sympletic vector bundles" Proc.Amer.Math.Soc.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Shyuichi Izumiya: "Topological properties of Legendrian singularities" Canadian Mathematical Bulletin. 34. 357-363 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Goo Ishikawa: "Parametrization of a singular Lagrangian variety" Trans.Amer.Math.Soc.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Nobuyuki Tose: "Morse inequalities for R-constructible sheaves" Advances in Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Isao Nakai: "Separatrices for conformal transformation groups of C,O" Ann.l'Inst Fourier.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Tatsuo Suwa: "Finite determinacy of analytic" Proc. Amer. Math. Soc. 112. 989-997 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Haruo Suzuki: "Chern-Simons-Maslov classes in some symplectic vector bundles" Proc. Amer. Math. Soc.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Shyuichi Izumiya: "Topological properties of Legendrian singularities" Canadian Math. Bull.34. 357-363 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Goo Ishikawa: "Parametrization of a singular Lagrangian variety" Trans. Amer. Math. Soc.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Nobuyuki Tose: "Morse inequalities for R-constructible sheaves" Advances in Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Isao Nakai: "Separatrices for conformal transformation groups of C, 0" Ann. i Inst. Fourier.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Tatsuo Suwa: "Finite determinacy of analytic foliation germs without formal integrating factors" Proc.Amer.Math.Soc.112. 989-997 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Haruo Suzuki: "ChernーSimonsーMaslov classes in some symplectic vector bundles" Proc.Amer.Math.Soc.

    • Related Report
      1991 Annual Research Report
  • [Publications] Shyuichi Izumiya: "Topological proterties of Legendrian singularities" Canadian Mathematical Bulletin. 34. 357-363 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Goo Ishikawa: "Parametrization of a singular Lagrangian variety" Trans.Amer.Math.Soc.

    • Related Report
      1991 Annual Research Report
  • [Publications] Nobuyuki Tose: "Morse inequalities for Rーconstructible sheaves" Advances in Math.

    • Related Report
      1991 Annual Research Report
  • [Publications] Isao Nakai: "Separatrices for conformal transformation groups of C,O" Ann.I'Intst.Fourier.

    • Related Report
      1991 Annual Research Report
  • [Publications] 諏訪 立雄: "Dーwodules associated to complex analytic siugular foliations" Journal of the Faculty of Science,the University of Tokyo. 37. 297-320 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] D.Cerveau: "Determinacy of complex analytic foliation gerws without integrating factors" Proceedings of the American Mathematical Society. (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 諏訪 立雄: "Structure of the singular set of a complex analytic foliation"

    • Related Report
      1990 Annual Research Report
  • [Publications] 中村 郁: "On surfaces of class VIIo with curues,II" To^^<^>hoku Mathematical Journal. 42. 475-516 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 泉屋 周一: "Topological properties of Legeadrian singularities" Canadian Mathematical Bulletiu.

    • Related Report
      1990 Annual Research Report
  • [Publications] 石川 剛郎: "Parawefrization of a singular Lagrangiar variety" Transactious of the American Mathematical Society.

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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