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Study on twistor spaces

Research Project

Project/Area Number 24540061
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionTokyo Institute of Technology (2014-2016)
Tohoku University (2012-2013)

Principal Investigator

Honda Nobuhiro  東京工業大学, 理工学研究科, 教授 (60311809)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsツイスター空間 / 有理多様体 / 二重被覆空間 / スカラー平坦ケーラー計量 / 反自己双対計量 / 線形系 / 分類 / 自己双対計量 / 代数次元 / 代数簡約
Outline of Final Research Achievements

The main topic of this investigation is to analyse structure of spaces which have background from Riemannian geometry and mathematical physics. This space is called twistor spaces, and is 3-dimensional object which can be descrbed using complex numbers. We intensively investigated geometric structure of twistor spaces. The main tool for the analysis is meromorphic functions on the twistor spaces. Namely I proved existence of meromorphic functions which are enough for describing structure of the spaces. In particular, I described a series of twistor spaces in terms of simple polynomials.

Report

(5 results)
  • 2016 Final Research Report ( PDF )
  • 2015 Annual Research Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 2013 2012 Other

All Int'l Joint Research (1 results) Journal Article (6 results) (of which Peer Reviewed: 5 results,  Open Access: 2 results,  Acknowledgement Compliant: 4 results) Presentation (7 results) (of which Int'l Joint Research: 3 results,  Invited: 7 results) Remarks (2 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Mary Immaculate College, Limerick(アイルランド)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Geometry of some twistor spaces of algebraic dimension one2015

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Complex Manifolds

      Volume: 2 Issue: 1 Pages: 105-130

    • DOI

      10.1515/coma-2015-0009

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Double solid twistor spaces II: general case2015

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Journal fuer die reine und angewandte Mathematik (Crelles Journal)

      Volume: 698 Issue: 698 Pages: 181-220

    • DOI

      10.1515/crelle-2013-0003

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Moishezon twistor spaces on 4CP^22014

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      Journal of Algebraic Geometry

      Volume: 23 Issue: 3 Pages: 471-538

    • DOI

      10.1090/s1056-3911-2013-00619-0

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Scalar flat Kaehler metric on affine bundles over CP^12014

    • Author(s)
      Nobuhiro Honda
    • Journal Title

      SIGMA

      Volume: 10

    • DOI

      10.3842/sigma.2014.046

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Deformation of LeBrun's ALE metrics with negative mass2013

    • Author(s)
      N. Honda and J. Viaclovsky
    • Journal Title

      Comm. Math. Phys.

      Volume: 322 Issue: 1 Pages: 127-148

    • DOI

      10.1007/s00220-012-1656-z

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Toric LeBrun metrics and Joyce metrics2013

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

      Geometry and Topology

      Volume: 17 Issue: 5 Pages: 2923-2934

    • DOI

      10.2140/gt.2013.17.2923

    • Related Report
      2013 Research-status Report
  • [Presentation] Moishezon twistor spaces2016

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Complex Geometry Seminar
    • Place of Presentation
      MSRI
    • Year and Date
      2016-03-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A remark on algebraic dimension of twistor spaces2015

    • Author(s)
      Nobuhiro Honda
    • Organizer
      多変数関数論冬セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2015-12-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some examples of twistor spaces of algebraic dimension one2015

    • Author(s)
      Nobuhiro Honda
    • Organizer
      Irish Geometry Conference 2015
    • Place of Presentation
      Mary Immaculate College, Limerick
    • Year and Date
      2015-05-15
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ツイスター空間の幾何学2015

    • Author(s)
      本多宣博
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Deformations of LeBrun's ALE metric with negative mass2013

    • Author(s)
      Nobuhiro Honda
    • Organizer
      The 8th Pacific Rim Complex Geometry Conference
    • Place of Presentation
      中国 大連工科大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] ツイスター理論2013

    • Author(s)
      本多宣博
    • Organizer
      第9回 秋葉原微分幾何セミナー
    • Place of Presentation
      東京理科大学理学部
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Deformations of LeBrun's ALE metrics with negative mass2012

    • Author(s)
      Nobuhiro Honda
    • Organizer
      第18回複素幾何シンポジウム
    • Place of Presentation
      信州菅平高原
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] publication list

    • URL

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

    • Related Report
      2015 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2014 Research-status Report
  • [Funded Workshop] Trends in Modern Geometry2015

    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2015-07-27
    • Related Report
      2015 Annual Research Report

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Published: 2013-05-31   Modified: 2019-07-29  

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