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Studies on moduli spaces from the view point of mathematical physics

Research Project

Project/Area Number 07304003
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section総合
Research Field Algebra
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

UENO Kenji  Kyoto Univ., Math.Dept., Professor, 大学院理学研究科, 教授 (40011655)

Co-Investigator(Kenkyū-buntansha) KATSURA Toshiyuki  Univ of Tokyo., Math.Dept., Professor, 大学院数理解科学研究科, 教授 (40108444)
MUKAI Shigeru  Nagoya Univ., Math.Dept., Professor, 大学院多元数理科学研究科, 教授 (80115641)
NAMIKAWA Yukihiko  Nagoya Univ., Math.Dept., Professor, 大学院多元数理科学研究科, 教授 (20022676)
JIMBO Michio  Kyoto Univ., Math.Dept., Professor, 大学院理学研究科, 教授 (80109082)
MARUYAMA Masaki  Kyoto Univ., Math.Dept., Professor, 大学院理学研究科, 教授 (50025459)
川又 雄二郎  東京大学, 大学院・数理科学研究科, 教授 (90126037)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥5,700,000 (Direct Cost: ¥5,700,000)
Fiscal Year 1996: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1995: ¥3,400,000 (Direct Cost: ¥3,400,000)
Keywordsmoduli space / conformal field theory / conformalblock vector bundle / Calabi-Yaumanifold / pointed Riemannsurface / arithmeticgeometry / q-analog / 弦理論 / 代数曲線 / ベクトル束のモジュライ空間 / リーマン面のモジュライ空間 / 単純リイ代数 / ゲージ対称性 / KZ方程式 / 閉リーマン面 / 共形場ブロック / ベクトル束 / 楕円曲面 / 変形理論
Research Abstract

Moduli spaces of algebraic varieties and vector bundles play am important role not only in algebraic geometry but also
mathematical physics. We studied moduli spaces from the view point of mathematical physics.
Ueno studied mainly conformal field theory which has deep relationship with moduli spaces of pointed Riemann surfaces. He showed that non-abelian conformal field theory, so called the WZW modelis defined overthe
rational number field and even more it can be defined over a discrete valuation ring. With Y.Shimizu and T.Suzuki he also studied explicit description of protectively flat connection of the sheaf of conformal blocks.
Maruyama showed a new method how to construct moduli sapce of stable sheaves on algebraic surfaces, which will play an important role to study boundaries of the moduli spaces. Mukai studied the moduli spaces of vector bundles on K3 surfaces and found interesting relationship with the moduli spaces of algebraic curves. Kawamata showed unobstractedness of deformations of Calabi-Yau manifolds by purely algebraic method. Katsura studied pluricanonical sytems of elliptic surfaces in positive characteristics and showed that they have similar properties as in characteristic O.
In this way we found many interesting properties of moduli spaces and also showed deep relationship with mathematicalphysics.

Report

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

Research Products

(32 results)

All Other

All Publications

  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(和文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications] 「研究成果報告書概要(欧文)」より

    • Related Report
      1996 Final Research Report Summary
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1996 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report
  • [Publications]

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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