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On families of algebraic varieties admitting unipotent group actions from the viewpoint of Minimal Model Program

Research Project

Project/Area Number 15K04805
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionSaitama University

Principal Investigator

KISHIMOTO Takashi  埼玉大学, 理工学研究科, 教授 (20372576)

Research Collaborator Adrien Dubouloz  
Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsユニポテント代数群 / シリンダー / 森ファイバー空間 / 極小モデル理論 / Fano多様体 / del Pezzoファイブレーション / affine extension / 1次元加法群スキーム / del Pezzo fibration / affine ruled / ユニポテント代数群作用
Outline of Final Research Achievements

We are interested in the following naturally looking problem "In which case, a given fibration between algebraic varieties whose general closed fibers admit effective unipotent group actions possesses an action the same group arising from those on general fibers ? ". This problem itself is quite difficult to accomplish completely, nevertheless we succeed into obtaining a certain sufficient condition. Meanwhile, by getting the above mentioned problem globalized, we consider the problem asking " Which kinds of Mori Fiber Spaces contain cylinders that are compatible with fiber structure ?" As for this problem, we know finally that the essence lies in behavior of the generic fibers, furthermore, we can obtain an effective criterion on the existence of cylinders depending on a given Mori Fiber Space.

Academic Significance and Societal Importance of the Research Achievements

本研究課題は純粋数学に関する研究に基づくものであるので,社会への直接的な貢献は見えづらく,主に研究代表者の知的好奇心により支えられている.しかし中長期的なスパンで見れば,代数幾何学の基礎研究は実生活への応用は起こり得る.(例えば代数曲線暗号理論はクレジットカードでネット経由で買い物をする時に本質的に役立っている.)

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (28 results)

All 2019 2018 2017 2016 2015 Other

All Int'l Joint Research (10 results) Journal Article (7 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 7 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (6 results) (of which Int'l Joint Research: 4 results,  Invited: 6 results) Book (1 results) Funded Workshop (4 results)

  • [Int'l Joint Research] Bourgogne大学・数学研究所(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Edinburgh大学(英国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Warwick大学(英国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] ポーランド科学アカデミー(ポーランド)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Bourgogne大学(フランス)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Edinburgh大学/Warwick大学(英国)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Bourgogne 大学(フランス)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Polish Academy of Science(ポーランド)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Uppsala 大学(スウェーデン)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Universite de Bourgogne(France)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Deformations of A^1-cylindrical varieties2019

    • Author(s)
      Adrien Dubouloz and Takashi Kishimoto
    • Journal Title

      Mathematische Annalen

      Volume: 印刷中 Issue: 3-4 Pages: 1135-1149

    • DOI

      10.1007/s00208-018-1774-9

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Equivariant extensions of Ga-torsors over punctured surfaces2019

    • Author(s)
      Adrien Dubouloz, Isac Heden and Takashi Kishimoto
    • Journal Title

      Annali della Scuola Normale Superiore de Pisa, Classe di Scienze

      Volume: 印刷中 Pages: 133-167

    • DOI

      10.2422/2036-2145.201710_002

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Cylinders in Mori Fiber Spaces: Forms of the quintic del Pezzo threefold2019

    • Author(s)
      Adrien Dubouloz and Takashi Kishimoto
    • Journal Title

      Annales de l’Institut Fourier

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Cylinders in del Pezzo fibrations2018

    • Author(s)
      Adrien Dubouloz and Takashi Kishimoto
    • Journal Title

      Israel Journal of Mathematics

      Volume: 225 Issue: 2 Pages: 797-815

    • DOI

      10.1007/s11856-018-1679-z

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Explicit biregular/birational geometry of affine threefolds: completions of A3 into del Pezzo fibrations and Mori conic bundles2017

    • Author(s)
      Dubouloz Adrien、Kishimoto Takashi
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 75 Pages: 49-71

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Explicit biregular/birational geometry of affine threefolds: completions of A3 into del Pezzo fibrations and Mori conic bundles2017

    • Author(s)
      Adrien Dubouloz and Takashi Kishimoto
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: ?

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Families of affine ruled surfaces: Existence of cylinders2016

    • Author(s)
      Adrien Dubouloz and Takashi Kishimoto
    • Journal Title

      Nagoya Mathematical Journal

      Volume: 223 Issue: 1 Pages: 1-20

    • DOI

      10.1017/nmj.2016.22

    • Related Report
      2016 Research-status Report 2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Forms of the quintic del Pezzo threefold V_52018

    • Author(s)
      Takashi Kishimoto
    • Organizer
      Algebraic Geometry-Mariusz Koras in memoriam, at Institute of Mathematics, Polish Academy of Sciences
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Cylinders in Mori Fiber Spaces: Forms of V52018

    • Author(s)
      Takashi Kishimoto
    • Organizer
      Polynomial Rings and Affine Algebraic Geometry
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Logarithmic Kodaira dimension and uniruledness2016

    • Author(s)
      Takashi KIshimoto
    • Organizer
      The 39th Autumn School in Algebraic Geometry: COMPLEX AFFINE GEOMETRY
    • Place of Presentation
      Lukecin, Poland
    • Year and Date
      2016-09-18
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Cylinders in Fano fibrations2016

    • Author(s)
      Takashi Kishimoto
    • Organizer
      射影多様体の幾何とその周辺2016
    • Place of Presentation
      高知工科大学 (高知県,高知市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Families of affine ruled surfaces: Existence of cylinders2016

    • Author(s)
      Takashi Kishimoto
    • Organizer
      International Workshop: Complex Affine Geometry,Hyperbolicity, Complex Analysis
    • Place of Presentation
      Institut Fourier (Grenoble, France)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Cylinders in del Pezzo fibrations2015

    • Author(s)
      Takashi Kishimoo
    • Organizer
      第60回代数学シンポジウム
    • Place of Presentation
      静岡大学(静岡県静岡市)
    • Year and Date
      2015-09-01
    • Related Report
      2015 Research-status Report
    • Invited
  • [Book] Advanced Studies in Pure Mathematics, Volume 75, Algebraic Varieties and Automorphism Groups2017

    • Author(s)
      Kayo Masuda, Takashi Kishimoto, Hideo Kojima, Masayoshi Miyanishi, Mikhail Zaidenberg
    • Total Pages
      474
    • Publisher
      Mathematical Society of Japan
    • ISBN
      9784864970488
    • Related Report
      2017 Research-status Report
  • [Funded Workshop] The17th Affine Algebraic Geometry Meeting2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Explicit Birational and Affine Algebraic Geometry in Saitama2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 第16回アフィン代数幾何学研究集会2018

    • Related Report
      2017 Research-status Report
  • [Funded Workshop] The 14th Affine Algebraic Meeting2016

    • Place of Presentation
      関西学院大学大阪梅田キャンパス
    • Year and Date
      2016-03-05
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2022-02-21  

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