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2001 Fiscal Year Final Research Report Summary

Research on arrangements of hyperplanes

Research Project

Project/Area Number 11440012
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Metropolitan Univ.

Principal Investigator

TERAO Hiroaki  Tokyo Metropolitan Univ., Department of Math., Professor, 理学研究科, 教授 (90119058)

Co-Investigator(Kenkyū-buntansha) TOKUNAGA Hiroo  Tokyo Metropolitan Univ., Department of Math., Assistant Professor, 理学研究科, 助教授 (30211395)
KAWASAKI Takeshi  Tokyo Metropolitan Univ., Department of Math., Assistant, 理学研究科, 助手 (40301410)
OKA Mutsuo  Tokyo Metropolitan Univ., Department of Math., Professor, 理学研究科, 教授 (40011697)
NAKAMURA Ken  Tokyo Metropolitan Univ., Department of Math., Professor, 理学研究科, 教授 (80110849)
NAKASHIMA Tooru  Tokyo Metropolitan Univ., Department of Math., Assistant Professor, 理学研究科, 助教授 (20244410)
Project Period (FY) 1999 – 2001
Keywordshyperplane arrangement / hyper geometric integral / local system cohomology / reflection group
Research Abstract

In the 2001 fiscal year, we obtained the following two major research results :
1. We showed that there exists a canonical basis for the module of vector fields tangent to a Coveter arrangement in a multiple order. We also showed the basis has deep relations with the flat structure of the orbit space.
2. We determined the structure of the differential module generated by reciprocals of linear forms. In particular, we obtained a formula for its Poincare series (to appear in J. Algebra).

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 寺尾宏明: "Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gaus-Manin connectious"Topology and its appl.. 118. 255-274 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岡睦雄: "Geometry of cuspidal sextics and their dual curves"Advanced Studies in Pure Math.. 29. 245-277 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岡睦雄: "Another involution on moduli of sextics"Kodai J.Math.. 24. 26-30 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 徳永浩雄: "Sextics with singular points in special positions"J.of Kuot theory and its ramifications. 10. 547-578 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川崎健: "On Arithmetic Macaulayfication of Noetherian Rings"Trans.Amer.Math.Soc. 354. 123-149 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中村憲: "Some results for some conjectures in addition chains"In Combinatrics, Computability and Logic, Proceedings of the Third International Conference on Combinatrics, Computability and Logic, (DMTCS'01). 47-54 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 徳永浩雄(共著): "代数曲線と特異点"共立出版. 363 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Terao, Hiroaki: "Moduli space of combinatorially equivalent arrange-ments of hyperplanes and logarithmic Gauss-Manin connections"Topol-ogy and its appl.. 118. 255-274 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Oka, Mutsuo: "Geometry of cuspidal sextics and their dual curves, Singularities - Sapporo"Advanced Studies in Pure Math. 29. 245-277 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Oka, Mutsuo: "Another involution on moduli of sextics"Kodai J. Math. Vol. 24, No.1. 26-30 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tokunaga, Hiroo: "Sextics with singular points in special positions"J. of Knot theory and its ramifications. 10. 547-578 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kawasaki, Takeshi: "On Arithmetic Macaulayfication of Noetherian Rings"Trans. Amer. Math. Soc.. 354. 123-149 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nakamula, Ken: "Some results for some conjectures in addition chains. In Combinatrics, Computability and Logic"Proceedings of the Third International Conference on Combinatrics, Computability and Logic, (DMTCS'01), pp. 47-54, Ovidius University Constantza, Romania, July 2001. Springer Verlag.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tokunaga, Hiroo: "Algebraic curves and singularities (Japanese)"Kyoritsu. 363 (2001)

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

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Published: 2003-09-17  

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