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Research on generalized geometric structures, 4 dimensional differential topology and derived category

Research Project

Project/Area Number 25610011
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionOsaka University

Principal Investigator

Goto Ryushi  大阪大学, 理学(系)研究科(研究院), 教授 (30252571)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords一般化された複素構造 / 一般化されたケーラー構造 / ポアソン構造 / 変形理論 / モジュライ空間 / flat structure / 非可換代数幾何 / 導来圏の変形 / 非可換曲面 / ツイスター空間 / 4次元多様体 / 一般化されたカラビーヤオ構造 / 超ケーラー多様体
Outline of Final Research Achievements

The author's results are mainly as follows. (1) We show that generalized complex structures on a complex surface induced from a holomorphic Poisson structure admit unobstructed deformations, i.e., the Kuranishi spaces are smooth. We construct moduli spaces of generalized complex structures induced from Poisson structures on del Pezzo surfaces. Further it turns out that the moduli space admits "Stratified flat structure", that is, the moduli space has a stratification which is constructed from the types of singularities of jumping locus and each strata admits a flat structure, i.e., a torsion free flat connection of the tangent bundle. (2) We obtain a new family of generalized complex structures with k connected components of jumping loci for any k on certain 4-manifolds which have neither complex structures and symplectic structures, by using logarithmic transformation of multiplicity m. These two results are already written in our paper [1] , [2] and they are accepted for publication.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (21 results)

All 2016 2015 2014 2013

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (12 results) (of which Int'l Joint Research: 1 results,  Invited: 10 results) Book (1 results) Funded Workshop (3 results)

  • [Journal Article] C^\infty logarithmic transformations and generalized complex structures2016

    • Author(s)
      R. Goto and K. Hayano
    • Journal Title

      The Journal of Symplectic Geometry

      Volume: -

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unobstructed deformations of generalized complex structures induced by C∞ logarithmic symplectic structures and logarithmic Poisson structures2016

    • Author(s)
      R. Goto
    • Journal Title

      Proceedings of China-Japan Geometry Conference: Geometry and Topology of Manifold ---The 10th Geometry Conference for the Friendship of China and Japan 2014

      Volume: -

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] C^\infty logarithmic transformations and generalized complex structures2015

    • Author(s)
      R. Goto
    • Journal Title

      J. Symplectic. Geom.

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the stability of locally conformal Kähler structures2014

    • Author(s)
      Goto, Ryushi
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 66 Issue: 4 Pages: 1375-1401

    • DOI

      10.2969/jmsj/06641375

    • NAID

      130004706004

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the stability of locally conformal Kaehler structures2014

    • Author(s)
      R. Goto
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 未定

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Stratified flat structures on moduli spaces of generalized complex surfaces2015

    • Author(s)
      R. Goto
    • Organizer
      The 21st Symposium Complex Geometry
    • Place of Presentation
      金沢大学サテライトプラザ
    • Year and Date
      2015-10-30
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Flat structures on moduli spaces of generalized complex surfaces2015

    • Author(s)
      R. Goto
    • Organizer
      東京大学数理科学研究科複素解析幾何セミナー
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2015-09-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] 対数的ポアソン構造と一般化された複素多様体の非障害的な変形について2015

    • Author(s)
      後藤竜司
    • Organizer
      東京工業大学大学院理工学研究科数学専攻大岡山談話会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2015-07-01
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 一般化された複素多様体と変形理論2015

    • Author(s)
      後藤竜司
    • Organizer
      東京工業大学 集中講義
    • Place of Presentation
      東京工業大学
    • Year and Date
      2015-06-29
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Unobstructed deformations of generalized complex structures induced by logarithmic Poisson structures2015

    • Author(s)
      R. Goto
    • Organizer
      満渕俊樹教授退職記念小研究会
    • Place of Presentation
      Osaka University
    • Year and Date
      2015-03-12
    • Related Report
      2014 Research-status Report
  • [Presentation] Unobstructed deformations of generalized complex structures induced by logarithmic Poisson structures2014

    • Author(s)
      R Goto
    • Organizer
      The 10th Geometry Conference for the Friendship between Chaina and Japan
    • Place of Presentation
      Shanghai, China
    • Year and Date
      2014-09-06 – 2014-09-12
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Deformations of generalized complex manifolds and locally conformally generalized kaehker structures2014

    • Author(s)
      R. Goto
    • Organizer
      Complex Geometry and Lie Groups
    • Place of Presentation
      Torino, Italy
    • Year and Date
      2014-06-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Deformations of generalized complex manifolds and locally conformally generalized K\"aher structures2014

    • Author(s)
      R. Goto
    • Organizer
      Complex Geometry and Lie Groups
    • Place of Presentation
      Torino 大学  イタリア
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Generalized complex structures on 4-manifolds and generalized hyperk\"ahler structures2013

    • Author(s)
      R. Goto
    • Organizer
      The Asian MAthematical Conference 2013,
    • Place of Presentation
      BEXCO, BUsan, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Generalized complex 4-manifolds and generalized Calabi-Yau metrical structure2013

    • Author(s)
      R. Goto
    • Organizer
      The 8th Pacific Rim Complex Geometry Conference
    • Place of Presentation
      Dalian, Liaoning, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Generalized complex structures and generalized Calabi-Yau metrics2013

    • Author(s)
      R. Goto
    • Organizer
      Symplectic Algebraic geometry
    • Place of Presentation
      Kansai seminar house, Kyoto
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Generalized contact structures and generalized Sasakian structures2013

    • Author(s)
      R. Goto
    • Organizer
      Tokyo-Seoul Conference in Mathematics -Differential Geometry-
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] 倉西数学への誘い2013

    • Author(s)
      藤木明、後藤竜司など
    • Total Pages
      21
    • Publisher
      岩波書店
    • Related Report
      2013 Research-status Report
  • [Funded Workshop] The 4th Workshop “Complex geometry and Lie Groups”2016

    • Place of Presentation
      奈良女子大学(奈良)
    • Year and Date
      2016-03-22
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] The 21st Symposium on Complex Geometry2015

    • Place of Presentation
      金沢サテライトプラザ(金沢)
    • Year and Date
      2015-10-28
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Japan-China Geometry Conference,2015

    • Place of Presentation
      京都大学(京都)、奈良女子大学(奈良)
    • Year and Date
      2015-09-07
    • Related Report
      2015 Annual Research Report

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Published: 2014-07-25   Modified: 2019-07-29  

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