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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 (1998)  Tokyo Metropolitan University, Graduate School of Sciences, Assistant, 大学院・理学研究科, 助手 (30264584)

寺尾 宏明 (1997)  北海道大学, 大学院・理学研究科, 教授 (90119058)

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)
中村 郁  北海道大学, 大学院・理学研究科, 教授 (50022687)
諏訪 立雄  北海道大学, 大学院・理学研究科, 教授 (40109418)
泉屋 周一  北海道大学, 大学院・理学研究科, 教授 (80127422)
齋藤 恭司  京都大学, 数理解析研究所, 教授 (20012445)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥6,800,000 (Direct Cost: ¥6,800,000)
Fiscal Year 1998: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1997: ¥4,200,000 (Direct Cost: ¥4,200,000)
Keywordshyperplane arrangement / hypergeometric integral / local system cohomology / reflection group / コクセタ-群
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).

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (50 results)

All Other

All Publications (50 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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [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
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 竹田雄一郎: "On the K-groups of spherical varieties" Osaka J.Math.35. 73-81 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 竹田雄一郎: "A relation between standard conjectures and their arithmetic aralogres" Kodai Math.J.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 岡 睦雄: "Smooth plane curves with one place at infinity" J.Math.Soc.Japan. 49.4. 663-687 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岡 睦雄: "Flex curves and their applications" Geometriae Dedicata. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 中村 憲: "Squares in binary recurrence sequences" Proceendings of the Number Theory Conference, Eger 1996. 409-421 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 中村 憲: "Recert developments of computational number theory" Number theory and its application, Kyoto 1997. 176-184 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "Connection matrices and Riemann-Hilbert problem for q-difference equations" Proc.of the 3rd Corference on Difference Equations and Its Appli, Taipei, Sept, 1997. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "Derivation of q-difference equation from Cannection matrix for Selberg type Jackson integrals" Jour.Difference Eq.and Its Appli. 4. 247-278 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "On elliptic product formulas for Jackson integrals associated with reduced root systems" Jour.Alg.Comb. 8. 115-126 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "On a Jacobian identity associated with real hyperplane arrangements" Composito Math. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "On quasi hypergeometric functions" Methods and Appli of Analysis. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "Singularity and monodromy of quasi hypergeometric functions" AMS Contempo.Math.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] ト部東介: "Duality of the second Fundamental form" Real analytic and algebraic singularities. 145-148 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 蔵野和彦: "On Macaulayfication obtained by ablow-up whose center is an equi-multiple ideal" J.of Alg.190. 405-434 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 蔵野和彦: "The positivity of intersection multiplicities and symbolic powers of prime ideals" Compositio Math. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 中村博昭: "Galois rigidity of pro-lpure braid groups an algebraic curves" Trans.Amer.Math.Soc.350. 1079-1102 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 中村博昭: "Limits of Galois representations in fundamental groups along maximal degeneration of a lgebraic curves I" Amer.J.Math.発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 青本和彦: "q-difference de Rham complex and Cech cohomology" Suugaku Expositions. 49 in Japanese. 350-364 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宮崎琢也: "The generalized Whittaker functions for Sp (2, R)" Proceedings of Japan Academy. 73. 130-133 (1977)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宮崎琢也: "Principal series Whittaker functions on Sp (2, R) II" Tohoku Mathematical Journal. 50. 243-260 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宮崎琢也: "The generalized Whittaker functions for Sp (2, R) and the gamma factor of the Andrianov's L-functions" J.of Math Sci, The Univ.of Tokyo. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 寺尾宏明: "Bnbc-bases for local system cohomology on hyperplane complements" Transactions AMS. 349. 189-202 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 寺尾宏明: "The determinant of ahypergeometric period matrix" Inventiones Math.128. 417-436 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 寺尾宏明: "Twisted de Rham cohondogy groups of logarithmic forms" Advances in Math.128. 119-152 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岡 睦雄: "Non-degenarate complete intensection singularity" Hermann, Paris, 309 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 諏訪立雄: "Indices of Vector Fields and Residues of Holomorphic Foliations" Hermann, Paris, (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 石川剛郎,泉屋周一: "応用特異点論" 共立出版, (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 中居功: "Web geometry and the eqwvalence problem of 1st order partial differential equations" フランス数学会(出版予定), (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 寺尾宏明: "Bnbc-bases for local system cohomdogy on hyperplane complements" Transactions AMS. 349. 189-202 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 寺尾宏明: "The determinant of a hypergeometric matrx" Inventiones mathematicae. 128. 417-436 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 青本和彦: "Tuisted de Rham Cohomology groups of logarithmic forms" Advances in Math.128. 119-152 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 寺尾宏明: "超平面配置と超幾何積分" 代数幾何学シンポジウム報告集. 1-9 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 寺尾宏明: "The double Coxeter arrangements" Commentarii Math.Helvetica. (印刷中).

    • Related Report
      1997 Annual Research Report
  • [Publications] 岡 睦雄: "Non-Degenerate Complete Intersection Singularity" Hermann, 309 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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