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Orbifold cohomology and generalization of the McKay correspondence

Research Project

Project/Area Number 19540022
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

ITO Yukari  Nagoya University, 多元数理科学研究科, 准教授 (70285089)

Co-Investigator(Kenkyū-buntansha) GUEST Martin  首都大学東京, 大学院・理工学研究科, 教授 (10295470)
MAENO Toshiaki  京都大学, 大学院・工学研究科, 講師 (60291423)
IRITANI Hiroshi  京都大学, 大学院・理学研究科, 准教授 (20448400)
Co-Investigator(Renkei-kenkyūsha) SATO Fumitoshi  香川高等専門学校, 講師 (20548309)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsトポロジー / マッカイ対応 / モジュライ空間 / 代数学 / 商特異点 / 幾何学 / 数理物理 / 特異点解消 / 特異点 / 有限群
Research Abstract

We studied on the ring structure and several properties of Orbifold cohomology and constructed crepant resolutions of Gorenstein singularities as moduli spaces of the quivers which are given by the representations of finite groups to see the generalized McKay correspondence.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (40 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 11 results) Presentation (22 results) Book (5 results)

  • [Journal Article] 「鏡の国へ行ってみよう!」~対称性のはなし~2011

    • Author(s)
      Yukari Ito
    • Journal Title

      日本数学会「数学通信」 15巻4号

      Pages: 20-30

    • NAID

      40018733087

    • Related Report
      2010 Final Research Report
  • [Journal Article] 「鏡の国へ行ってみよう!」~対称性のはなし~2011

    • Author(s)
      伊藤由佳理
    • Journal Title

      日本数学会「数学通信」

      Volume: 15巻4号 Pages: 20-30

    • NAID

      40018733087

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Ruan's conjecture and integral structures in quantum cohomology. New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry(RIMS, Kyoto, 2008)2010

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      Adv.Stud.Pure Math. 59

      Pages: 111-166

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The tt* Structure of the Quantum Cohomology of CP1 from the Viewpoint of Differential Geometry2010

    • Author(s)
      J.Dorfmeister, M.Guest, W.Rossman
    • Journal Title

      Asian Jour.Math. 14

      Pages: 417-438

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials2009

    • Author(s)
      Toshiaki Maeno, Junzo Watanabe
    • Journal Title

      Illinois J.Math. 53

      Pages: 591-603

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wall-crossings in toric Gromov-Witten theories I, Crepant examples.2009

    • Author(s)
      Tom Coates, Hiroshi Iritani, Hsian-Hua Tseng
    • Journal Title

      Geometry and Topology 13, no.5

      Pages: 2675-2744

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Computing genus zero twisted Gromov-Witten invariants.2009

    • Author(s)
      Tom Coates, Alessio Corti, Hiroshi Iritani, Hsian-Hua Tseng
    • Journal Title

      Duke Math.J. 147, no.3

      Pages: 377-438

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An integral structure in quantum cohomology and mirror symmetry for toric orbifolds.2009

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      Adv.Math. 222, no.3

      Pages: 1016-1079

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Recursive formula for $\psi^g-\lambda_1 \psi^{g-1}+\cdots+(-1)^g\lambda_g$ in $\overline{M}_{g,1}$''2009

    • Author(s)
      Arcara, D., Sato, F.
    • Journal Title

      Proc.of Amer.Math.Soc. vol.137, No.12

      Pages: 4077-4081

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Schur-Weyl duality and a q-deformation of Specht polynomial2007

    • Author(s)
      Toshiaki Maeno
    • Journal Title

      Comm.Alg 35

      Pages: 1307-1321

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of quantum cohomology by quantum Lefschetz2007

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      J.Reine.Angew.Math 610

      Pages: 29-69

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Schur-Weyl duality and a q-deformation of Specht polynomial2007

    • Author(s)
      Toshiaki Maeno
    • Journal Title

      Comm. Alg 35

      Pages: 1307-1321

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of quantum cohomology by quantum Lefschetz2007

    • Author(s)
      Hiroshi Iritani
    • Journal Title

      J. Reine. Angew. Math. 610

      Pages: 29-69

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Alcove pathとaffine Weyl群上の非可換微分構造2011

    • Author(s)
      Toshiaki Maeno
    • Organizer
      日本数学会年会の中止に伴う臨時講演会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Final Research Report
  • [Presentation] マッカイ対応入門2010

    • Author(s)
      Yukari Ito
    • Organizer
      情報数理談話会
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2010-12-21
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 「鏡の国へ行ってみよう!」~対称性のはなし~2010

    • Author(s)
      Yukari Ito
    • Organizer
      日本数学会市民講演会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-26
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Troidal resolution of non-abelian quotient singularities2010

    • Author(s)
      Yukari Ito
    • Organizer
      Geometry and Algebra of Orbifolds and the McKay Correspondence
    • Place of Presentation
      ウォーリック大学(イギリス)
    • Year and Date
      2010-08-12
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] McKay対応入門I, II2010

    • Author(s)
      Yukari Ito
    • Organizer
      静岡大学代数学セミナー
    • Place of Presentation
      静岡大学
    • Year and Date
      2010-07-02
    • Related Report
      2010 Final Research Report
  • [Presentation] McKay対応入門I, II2010

    • Author(s)
      伊藤由佳理
    • Organizer
      第7回静岡代数学セミナー
    • Place of Presentation
      静岡大学
    • Year and Date
      2010-07-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] On Hilb of Hilb2010

    • Organizer
      研究集会 "Seminar on McKay correspondence"(Join work with Alvaro Nolla de Celis)
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-03-09
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Hilb of Hilb2010

    • Author(s)
      伊藤由佳理
    • Organizer
      Seminar on McKay correspondence
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-03-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Existence of crepant resolutions2009

    • Author(s)
      Yukari Ito
    • Place of Presentation
      ソガン大学(韓国)
    • Year and Date
      2009-08-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Existence of crepant resolutions2009

    • Organizer
      代数幾何学セミナー
    • Place of Presentation
      韓国・ソガン大学
    • Year and Date
      2009-08-07
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Exsistence of crepant resolutions2009

    • Author(s)
      伊藤由佳理
    • Organizer
      代数幾何学セミナー
    • Place of Presentation
      ソガン大学(韓国/ソウル)
    • Year and Date
      2009-08-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Quantum cohomology D-modules of toric stacks2009

    • Author(s)
      Hiroshi Iritani
    • Organizer
      Equivariant Gromov-Witten theory and symplectic vortices
    • Place of Presentation
      C.I.R.M. Marseille-Luminy
    • Year and Date
      2009-07-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Existenoe of crepant resolutions2008

    • Author(s)
      Yukari Ito
    • Organizer
      COE COW Tokyo.
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-18
    • Related Report
      2010 Final Research Report
  • [Presentation] Existence of crepant resolutions2008

    • Organizer
      COE COW Tokyo
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-18
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Existenoe of crepant resolutions2008

    • Author(s)
      伊藤由佳理
    • Organizer
      COE COW Tokyo
    • Place of Presentation
      東京大学
    • Year and Date
      2008-12-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] Existence of crepant resolutions2008

    • Author(s)
      Yukari Ito
    • Organizer
      WAG Concluding Conference.
    • Place of Presentation
      ウォーリック大学(イギリス)
    • Year and Date
      2008-07-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Existence of crepant resolutions2008

    • Organizer
      Warwick Algebraic Geometry Concluding Conference
    • Place of Presentation
      イギリス・ウォーリック大学
    • Year and Date
      2008-07-23
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Existence of crepant resolutions2008

    • Author(s)
      伊藤由佳理
    • Organizer
      WAG Concluding Conference
    • Place of Presentation
      ウォーリック大学(イギリス)
    • Year and Date
      2008-07-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] The existence of crepant resolutions2008

    • Author(s)
      Yukari Ito
    • Organizer
      Mathematics and Physics seminar.
    • Place of Presentation
      ペンシルバニア大学(アメリカ合衆国)
    • Year and Date
      2008-02-29
    • Related Report
      2010 Final Research Report
  • [Presentation] The existence of crepant resolutions2008

    • Organizer
      Mathematics and Physics Seminar
    • Place of Presentation
      アメリカ・ペンシルバニア大学
    • Year and Date
      2008-02-29
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] The existence of crepant resolutions2008

    • Author(s)
      Yukari Ito
    • Organizer
      Mathematics and Physics seminar
    • Place of Presentation
      ペンシルバニア大学
    • Year and Date
      2008-02-29
    • Related Report
      2007 Annual Research Report
  • [Presentation] tt*-geometry

    • Author(s)
      Martin Guest
    • Organizer
      Progress on Surface Theory
    • Place of Presentation
      MFI Oberwolfach(ドイツ)
    • Related Report
      2010 Final Research Report
  • [Book] Special McKay correspondence「Singularity Seminar 2008」多元数理講義録2009

    • Author(s)
      Yukari Ito
    • Related Report
      2009 Self-evaluation Report
  • [Book] この定理が美しい2009

    • Author(s)
      伊藤由佳理, 他19名
    • Total Pages
      200
    • Publisher
      数学書房
    • Related Report
      2009 Annual Research Report
  • [Book] From Quantum cohomology to Integrable Systems2008

    • Author(s)
      Martin Guest
    • Total Pages
      305
    • Publisher
      Oxford Univ.(Press.)
    • Related Report
      2010 Final Research Report
  • [Book] From Quantum cohomology to Integrable Systems2008

    • Author(s)
      Martin Guest
    • Total Pages
      305
    • Publisher
      Oxford Univ. Press
    • Related Report
      2007 Annual Research Report
  • [Book] この定理が美しい(共著)

    • Author(s)
      伊藤由佳理
    • Publisher
      数学書房
    • Related Report
      2010 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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