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Study on twistor spaces

Research Project

Project/Area Number 16H03932
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Institute of Technology

Principal Investigator

Honda Nobuhiro  東京工業大学, 理学院, 教授 (60311809)

Project Period (FY) 2016-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥10,530,000 (Direct Cost: ¥8,100,000、Indirect Cost: ¥2,430,000)
Fiscal Year 2020: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywordsツイスター空間 / 二重被覆写像 / 双有理変換 / 有理多様体 / ミニツイスター空間 / 自己双対計量 / 代数多様体 / 通常二重点 / 双対多様体 / 代数空間 / 二重被覆 / デルペッツォ曲面 / 曲面束 / 順像層 / 4次超曲面 / Del Pezzo 曲面 / Del Pezzo曲面束 / 反自己双対計量 / 非ケーラー多様体
Outline of Final Research Achievements

The twistor spaces associated with 4-dimensional compact self-dual manifolds are 3-dimensional compact complex manifolds. Most of them do not admit a Kahler metric, and moreover, they are known to be non-algebraic (in the sense that they are not bimeromorphic to projective algebraic varieties). In this study, we investigate the structure of compact twistor spaces that do not have a Kahler metric but are algebraic (in the sense that they are bimeromorphic to projective algebraic varieties). For any given twistor space, there is a linear system called the fundamental system, and it was known that the structure of the twistor space is considerably limited by the structure of a divisor belonging to the fundamental system. In this study, we obtained a structure theorem for algebraic compact twistor spaces such that the fundamental system is of dimension one or more.

Academic Significance and Societal Importance of the Research Achievements

自己双対計量とツイスター空間の研究はペンローズにより、物理現象を複素数を用いた幾何学、すなわち複素幾何により理解する目的で始められたが、そこで見出された方法や対象は純粋数学においても多くの応用や成果をもたらした。本研究はツイスター理論を純粋数学における対象として考察するものである。このような研究は世界的に見てあまりなされておらず、独自性があるものだと思われる。また本研究で最終的に得られた構造定理は(当初の予想に反して)かなりシンプルなものである。

Report

(6 results)
  • 2022 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (19 results)

All 2022 2019 2018 2017 2016 Other

All Int'l Joint Research (1 results) Journal Article (4 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 4 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (8 results) (of which Int'l Joint Research: 3 results,  Invited: 5 results) Remarks (4 results) Funded Workshop (2 results)

  • [Int'l Joint Research] Mary Immaculate College(Ireland)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Segre quartic surfaces and minitwistor spaces2022

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      New York J. Math.

      Volume: 28 Pages: 672-704

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the cuspidal locus in the dual varieties of Segre quartic surface2022

    • Author(s)
      Nobuhiro Honda, Ayato Minagawa
    • Journal Title

      Riv. Mat. Univ. Parma 13.

      Volume: 13 Pages: 551-610

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Algebraic dimension of twistor spaces whose fundamental system is a pencil2017

    • Author(s)
      Honda Nobuhiro、Kreussler Bernd
    • Journal Title

      Journal of the London Mathematical Society

      Volume: 95 Issue: 3 Pages: 989-1010

    • DOI

      10.1112/jlms.12043

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Algebraic dimension of twistor spaces whose fundamental system is a pencil.2017

    • Author(s)
      Nobuhiro Honda and Bernd Kreussler
    • Journal Title

      J. London Math. Soc.

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] A new family of space-like Zoll 3-manifolds2022

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Workshop on Complex geometry in Osaka 2022
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Twistors, quartics, and del-Pezzo vibrations2019

    • Author(s)
      本多宣博
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Toward classification of Moishezon twistor spaces2019

    • Author(s)
      本多宣博
    • Organizer
      複素解析幾何セミナー(東大駒場)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Twistors, quartics, and del Pezzo fibrations2019

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Workshop on Global Aspects of Projective and Kahler Geometry
    • Related Report
      2018 Annual Research Report
  • [Presentation] wistor spaces, Del Pezzo fibrations, and quartic hypersurfaces2018

    • Author(s)
      本多宣博
    • Organizer
      中央大学 幾何・トポロジーセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Twistor spaces, Del Pezzo fibrations, and quartic hypersurfaces2018

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Cohomology of Complex Manifolds and Special Structures
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Twistors, quartics, and del Pezzo fibrations2018

    • Author(s)
      Nobuhiro Honda
    • Organizer
      The 24th Symposium on Complex Geometry
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Algebraic Geometry of Twistor Spaces2016

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Conference on Differential Geometry
    • Place of Presentation
      CRM, Montreal
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] Research Papers

    • URL

      http://www.math.titech.ac.jp/~honda/publicationlist.html

    • Related Report
      2020 Annual Research Report
  • [Remarks] ホームページ

    • URL

      http://www.math.titech.ac.jp/~honda/index.html

    • Related Report
      2019 Annual Research Report
  • [Remarks] Honda's web page

    • URL

      http://www.math.titech.ac.jp/~honda/index.html

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.titech.ac.jp/~honda/index.html

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Trends in Modern Geometry2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] Trends in Modern Geometry2016

    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2016-07-21
    • Related Report
      2016 Annual Research Report

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Published: 2016-04-21   Modified: 2024-01-30  

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