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Explicit construction of twistor spaces

Research Project

Project/Area Number 21740043
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTohoku University (2010-2011)
Tokyo Institute of Technology (2009)

Principal Investigator

HONDA Nobuhiro  東北大学, 大学院・理学研究科, 准教授 (60311809)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsツイスター空間 / 自己双対計量 / ミニツイスター空間 / Einstein-Weyl構造 / 共形構造 / 線形系 / 双有理変換 / Moishezon多様体 / 有理写像 / 二重被覆 / 分岐因子
Research Abstract

We have constructed various examples of algebraic twistor spaces in explicit forms, and given a characterization of them in terms of the corresponding self-dual metrics. Also we have refined the definition of minitwistor twistor spaces, and constructed various examples satisfying that property. In particular, we have constructed minitwistor spaces which are obtained from the so called Joyce metrics. There minitwistor spaces are rational surfaces which have simple structure, but usually have singularities. Moreover, we have concretely described some degenerations for significantexamples of some algebraic twistor spaces.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (51 results)

All 2012 2011 2010 2009 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results) Presentation (30 results) Remarks (3 results)

  • [Journal Article] Conformal symmetries of self-dual hyperbolic monopole metrics2012

    • Author(s)
      Nobuhiro Honda, Jeff Viaclovsky
    • Journal Title

      Osaka J.Math.

      Volume: (未定)(印刷中)

    • NAID

      120005986470

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Twistor spaces and self-dual metrics2011

    • Author(s)
      N. Honda
    • Journal Title

      Sugaku Expositions 24

      Volume: no. 1 Pages: 123-143

    • NAID

      130004558872

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Degenerations of LeBrun twistor spaces2011

    • Author(s)
      N. Honda
    • Journal Title

      Comm. Math. Phys. 301

      Volume: no.3 Pages: 749-770

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minitwistor spaces, Severi varieties, and Einstein-Weyl structure2011

    • Author(s)
      N. Honda and Fuminori Nakata
    • Journal Title

      Ann. Global Anal. Geom. 39

      Volume: no.3 Pages: 293-323

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minitwistor spaces, Severi varieties, and Einstein-Weyl structure2011

    • Author(s)
      Nobuhiro Honda, Fuminori Nakata
    • Journal Title

      Ann.Global Anal.Geom.

      Volume: 39 Issue: 3 Pages: 293-323

    • DOI

      10.1007/s10455-010-9235-z

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Degenerations of LeBrun twistor spaces2011

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Comm.Math.Phys

      Volume: 301 Issue: 3 Pages: 749-770

    • DOI

      10.1007/s00220-010-1165-x

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Degenerations of LeBrun twistor spaces2011

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Comm.Math.Phys.

      Volume: 301 Pages: 749-770

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On pluri-half-anticanonical system of LeBrun twistor spaces2010

    • Author(s)
      N. Honda
    • Journal Title

      Proc. Amer.Math. Soc

      Volume: 138 Pages: 2051-2060

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] New examples of minitwistor spaces and their moduli space2010

    • Author(s)
      N. Honda
    • Journal Title

      Osaka J. Math

      Volume: 47 Pages: 717-730

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new series of compact minitwistorspaces and Moishezon twistor spaces over them2010

    • Author(s)
      N. Honda
    • Journal Title

      J. reine angew. Math

      Volume: 642 Pages: 197-235

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On pluri-half-anticanonical system of LeBrun twistor spaces2010

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 138 Pages: 2051-2060

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new series of compact minitwistor spaces and Moishezon twistor spaces over them2010

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      J.reine angew.Math.

      Volume: 642 Pages: 197-235

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New examples of minitwistor spaces and their moduli space2010

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Osaka J.Math.

      Volume: 47 Pages: 717-730

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On pluri-half-anticanonical system of LeBrun twistor spaces2010

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Proceeding of American Mathematical Society 138

      Pages: 2051-2060

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A new series of compact minitwistorspaces and Moishezon twistor spaces over them2010

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      J.reine angew. Math (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Explicit construction of new Moishezon twistor spaces2009

    • Author(s)
      N. Honda
    • Journal Title

      J. Differential Geom. 82

      Volume: no.2 Pages: 411-444

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a construction of the twistor spaces of Joyce metrics2009

    • Author(s)
      N. Honda
    • Journal Title

      II. J. Math. Soc. Japan. 61.

      Volume: no.4 Pages: 1243-1260

    • NAID

      120003728346

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a construction of the twistor spaces of Joyce metrics, II2009

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Journal of Mathematical Society of Japan 61

      Pages: 1243-1260

    • NAID

      10026998725

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 4CP2上のMoishezonツイスター空間の分類2012

    • Author(s)
      本多宣博
    • Organizer
      日本数学会2012年年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 4CP2上のMoishezonツイスター空間の分類2012

    • Author(s)
      Nobuhiro Honda
    • Organizer
      日本数学会2012年年会
    • Place of Presentation
      東京理科大学理学部
    • Year and Date
      2012-03-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Toward classification of Moishezon twistor spaces2012

    • Author(s)
      本多宣博
    • Organizer
      藤木明先生 退職記念研究集会
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2012-03-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Toward classification of Moishezon twistor spaces2012

    • Author(s)
      Nobuhiro Honda
    • Organizer
      藤木明先生退職記念研究集会
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2012-03-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Deformation of LeBrun's ALEmetric with negative mass2012

    • Author(s)
      本多宣博
    • Organizer
      仙台小研究集会
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2012-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Deformation of LeBrun's ALE metric with negative mass2012

    • Author(s)
      Nobuhiro Honda
    • Organizer
      仙台小研究集会
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2012-03-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] Classification of Moishezon twistor spaces on 4CP^22012

    • Author(s)
      Nobuhiro Honda
    • Organizer
      東北大学幾何セミナー
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2012-01-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Geometry of twistor spaces2011

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Colloquium at Department of Mathematics, Fudan University
    • Place of Presentation
      上海、中国
    • Year and Date
      2011-12-01
    • Related Report
      2011 Final Research Report
  • [Presentation] Geometry of twistor spaces2011

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Colloquium at Department of Mathematics, Fudan University
    • Place of Presentation
      Fudan University (China)
    • Year and Date
      2011-12-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] Double solid twistor spaces2011

    • Author(s)
      Nobuhiro Honda
    • Organizer
      第17回複素幾何シンポジウム
    • Place of Presentation
      長野県菅平高原
    • Year and Date
      2011-11-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Double solid twistor spaces2011

    • Author(s)
      Nobuhiro Honda
    • Organizer
      第17回複素幾何シンポジウム(長野県菅平)
    • Place of Presentation
      長野県菅平高原ゾンタック
    • Year and Date
      2011-11-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Classification of Moishezon twistor spaces on 4CP^22011

    • Author(s)
      本多宣博
    • Organizer
      東京大学複 素解析幾何セミナー
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-10-31
    • Related Report
      2011 Final Research Report
  • [Presentation] Classification of Moishezon twistor spaces on 4CP^22011

    • Author(s)
      Nobuhiro Honda
    • Organizer
      東京大学複素解析幾何セミナー
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-10-31
    • Related Report
      2011 Annual Research Report
  • [Presentation] Classification of algebraic twistor spaces on 4CP^22011

    • Author(s)
      本多宣博
    • Organizer
      京都大学微分トポロジーセミナー
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2011-02-10
    • Related Report
      2011 Final Research Report
  • [Presentation] Classification of algebraic twistor spaces on 4CP^22011

    • Author(s)
      本多宣博
    • Organizer
      京都大学微分トポロジーセミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2011-02-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Moishezonツイスター空間について2010

    • Author(s)
      本多宣博
    • Organizer
      大阪大学数学教室談話会
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2010-12-06
    • Related Report
      2011 Final Research Report
  • [Presentation] Geometry of generic Moishezon twistor spaces on 4CP^22010

    • Author(s)
      本多宣博
    • Organizer
      大阪大学数学教室幾何セミナー
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2010-12-06
    • Related Report
      2011 Final Research Report
  • [Presentation] Geometry of generic Moishezon twistor spaces on 4CP^22010

    • Author(s)
      本多宣博
    • Organizer
      東北大学数学教室幾何セミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2010-12-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Geometry of generic Moishezon twistor spaces on 4CP^22010

    • Author(s)
      本多宣博
    • Organizer
      大阪大学数学教室幾何セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2010-12-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Moishezonツイスター空間について2010

    • Author(s)
      本多宣博
    • Organizer
      大阪大学数学教室談話会
    • Place of Presentation
      大阪大学
    • Year and Date
      2010-12-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Geometry of genericMoishezon twistor spaces on 4CP^22010

    • Author(s)
      本多宣博
    • Organizer
      東北大学数学教室幾何セミナー
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2010-11-09
    • Related Report
      2011 Final Research Report
  • [Presentation] 自己双対多様体のツイスター空間について2010

    • Author(s)
      本多宣博
    • Organizer
      日本数学会2010年度秋季総合分科会幾何学分科会特別講演
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] The minitwistor spaces of Joyce metrics2010

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Geometry Seminar, Department of Mathematics, Tsinghua University
    • Place of Presentation
      北京(中国)
    • Year and Date
      2010-09-14
    • Related Report
      2011 Final Research Report
  • [Presentation] The minitwistor spaces of Joyce metrics2010

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Geometry Seminar, Department of Mathematics
    • Place of Presentation
      清華大学、北京中国
    • Year and Date
      2010-09-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Generic Moishezon twistor spaces on 4CP^22010

    • Author(s)
      Nobuhiro Honda
    • Organizer
      The 6th Geometry Conference for Friendship of China and Japan
    • Place of Presentation
      西安(中国)
    • Year and Date
      2010-09-04
    • Related Report
      2011 Final Research Report
  • [Presentation] Generic Moishezon twistor spaces on 4CP^22010

    • Author(s)
      Nobuhiro Honda
    • Organizer
      The 6th Geometry Conference for Friendship of China and Japan
    • Place of Presentation
      西安、中国
    • Year and Date
      2010-09-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Joyce計量から生じるミニツイスター空間2010

    • Author(s)
      本多宣博
    • Organizer
      第57回幾何学シンポジウム
    • Place of Presentation
      神戸大学
    • Year and Date
      2010-08-09
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] 自己双対計量とツイスター空間2010

    • Author(s)
      本多宣博
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村南阿蘇(阿蘇くじゅう国立公園)
    • Related Report
      2011 Final Research Report
  • [Presentation] 自己双対計量とツイスター空間2010

    • Author(s)
      本多宣博
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村南阿蘇
    • Related Report
      2010 Annual Research Report
  • [Presentation] Degenerations of LeBrun twistor spaces2009

    • Author(s)
      本多宣博
    • Organizer
      筑波大学微分幾何学研究集会
    • Place of Presentation
      筑波大学
    • Year and Date
      2009-12-19
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2010 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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