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Mathematics on manifolds

Research Project

Project/Area Number 07304059
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section総合
Research Field Algebra
Research InstitutionTohoku University

Principal Investigator

ODA Tadao  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (60022555)

Co-Investigator(Kenkyū-buntansha) MIYANISHI Masayoshi  Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80025311)
MASAKI Maruyama  Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50025459)
HIJIKATA Hiroaki  Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00025298)
SHIODA Tetsuji  Rikkyo University, Faculty of Science, Professor, 理学部, 教授 (00011627)
SUNADA Toshikazu  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20022741)
北岡 良之  名古屋大学, 大学院・多元数理科学研究科, 教授 (40022686)
隅広 秀康  広島大学, 理学部, 教授 (60068129)
上野 健爾  京都大学, 大学院・理学研究科, 教授 (40011655)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 1996: ¥4,000,000 (Direct Cost: ¥4,000,000)
Keywordsalgebraic geometry / arithmetic geometry / analytic geometry / toric geometry / logarithmic geometry / lattice model / category / global analysis on graphs / 対数的幾何学 / グラフ / ホッジ理論 / 大域解析 / 代数幾何学 / ヘッケ環 / 特異点理論 / 結び目 / 絡み目
Research Abstract

Through close contact and discussion among the investigators, comprehensive study was made on various problems on manifolds mainly from algebraic perspective, but with enough consideration made of methods and perspective in geometry and analysis.
The following symposia and workshops were organized to discuss results obtained around the investigators on algebraic geometry, arithmetic geometry, analytic geometry, toric geometry, logarithmic geometry, lattice models, Hecke algebras, singularities, knots, category, global analysis on graphs, etc.
1.Algebraic Geometry Symposium (January 16-19,1996, Kawai Hall, Tohoku University).
2.Workshop on Solvable Lattice Models and Hecke Algebras (January 16-19,1996, Mathematical Institute, Tohoku University).
3.Workshop on Algebraic Geometry and Topology of Degenerations, Singularities and Coverings (February 10-13,1996, Faculty of Engineering, Tohoku Gakuin University).
4.Symposium on Hodge Theory and Algebraic Geometry (June 18-21,1996, Kawai Hall, Tohoku University).
5.Symposium on Cathegorical Methods and Non-Classical Logics (July 15-17,1996, Kawai Hall, Tohoku University).
6.Symposium on Geometric Spectral Problems (September 5-7,1996, Mathematical Institute, Tohoku University).
7.Mini-workshop on Log Geometry (October 30- November 1, Mathematical Institute, Tohoku University).

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (29 results)

All Other

All Publications (29 results)

  • [Publications] Tadao ODA: "Recent topics on toric Varieties" Amer.Math.Soc.Transl.(2). 172. 77-91 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tetsuji SHIODA: "A uniform construction of the root latlices E_6,E_7,E_8 dusl latlias and their" Proc.Japan Acad.71. 140-143 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Hiroaki HIJIKATA: "On the decomposition of latlices over orders" J.Math.soc.Japan. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Masayoshi MIYANISHI: "Recent topics on open algebraic surfaces" Amer.Moth.Soc.Trausl.(2). 172. 61-76 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Masaki MARUYAMA: "Instantons and parabolei sheaves" Rroc.Infery.Collog.on Geometry and Aualysio. 245-268 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kenji UENO: "Neron-Severi groups for torus guasi bundles over curols" Lechure Nofes in Pure and Appl.Math.179. 11-32 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.SUNADA and P.W.SY: "Geometry and Aualysis on Graphs" Cambridge University Press(発行予定), 250

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tadao ODA: "Recent topics on touric varieties." Amer.Math.Soc.Transl.(2), 172. 77-91 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tetsuji SHIODA: "A uniform construction of the root lattices E_6, E_7, E_8 and their dual lattices." Proc.Japan Acad.71. 140-143 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Hiroaki HIJIKATA: "On the decomposition of lattices over orders." J.Math.Soc.Japan.(to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Masayoshi MIYANISHI: "Recent topics on open algebraic surfaces." Amer.Math.Soc.Transl.(2), 172. 61-76 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Masaki MARUYAMA: "Instantons and parabolic sheaves." Proc.Intern.Colloq.on Geoemtry and Analysis. 245-268 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Kenji UENO: "Neron-Severi groups for torus quasi bundles over curves." Lecture Notes in Pure and Appl.Math.179. 11-32 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Toshikazu SUNADA and P.W.SY.: "Geometry and Analysis on Graphs." Cambridge Univ.Press. (to appear.). 250

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tadao ODA: "Recent topics on toric varieties" Amer.Math.Soc.Transl.(2). 172. 77-91 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Tetsuji SHIODA: "The algebraic equation of type E_6 and Chebotarey density" Algebra and Analysis (Arslanov et al., eds.). 109-114 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Yoshiyuki KITAOKA: "The minimum and the primitive representation of positive definite forms, II" Nagoya Math.J.141. 1-27 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Hiroaki HIJIKATA: "On the decomposition of lattices over orders" J.Math.Soc.of Japan. 49(発表予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] Masaki MARUYAMA: "Construction of moduli spaces of stable sheaves via Simpson's idea" Proc.Taniguchi Symp., M.Debker. 49-89 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Masayoshi MIYANISHI: "Recent yopics on open algebraic surfaces" Amer.Math.Soc.Transl.(2). 172. 61-76 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Sunada and P.W.Sy: "Geometry and Analysis on Graphs" Cambridge University Press(出版予定), 250

    • Related Report
      1996 Annual Research Report
  • [Publications] Tadao ODA: "Recent topics on toric varieties" Amer.Math.Soc.Transl.(2). 172. 77-91 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Tetsuji SHIODA: "Weierstrass teansformations and cubic surfaces" Comment.Math.Univ.St.Pauli. 44. 109-128 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Yoshiyuki KITAOKA: "The minimum and the primituie reyrescutotion of positiveg.f." Nagoya Math.J.発表予定.

    • Related Report
      1995 Annual Research Report
  • [Publications] Hiroaki HIJIKATA: "Decomposition of lattices over orders" J.Math.Soc.Japan. 発表予定.

    • Related Report
      1995 Annual Research Report
  • [Publications] Masayoshi MIYANISHI: "Recent topics on open algebraic surfaces" Amer.Math.Soc.Transl.(2). 172. 61-76 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Katsumi SHIRATANI: "On a rationality problew of Jacobisums" Acta Arith. 発表予定. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 堀田,良之: "D加群と代数群" シュプリンガー東京, 310 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 上野,健爾: "代数幾何入門" 岩波書店, 345 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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