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Several aspects of birational automorphisms of algebraic varieties

Research Project

Project/Area Number 15H03611
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Tokyo (2016-2019)
Osaka University (2015)

Principal Investigator

Oguiso Keiji  東京大学, 大学院数理科学研究科, 教授 (40224133)

Co-Investigator(Kenkyū-buntansha) 高木 俊輔  東京大学, 大学院数理科学研究科, 教授 (40380670)
權業 善範  東京大学, 大学院数理科学研究科, 准教授 (70634210)
川又 雄二郎  東京大学, 大学院数理科学研究科, 教授 (90126037)
Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000)
Fiscal Year 2019: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2018: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2017: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2015: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Keywords原始的自己同型 / 力学次数 / エントロピー / エンリケス曲面 / 離散的自己同型群の有限生成性 / 複素代数多様体の実形式 / 代数多様体の自己同型群 / ワイルドな自己同型 / 代数多様体 / 自己射 / 自己同型群 / 非有限生成性 / 台数多様体 / 双有理自己射 / ダイナミカル次数 / 双有理変換 / カラビ・ヤウ多様体 / 有理多様体 / 自己同型 / 原始的自己写像 / 代数多様体の自己射 / 超ケーラー多様体 / 単有理多様体 / 双有理変換群 / 複素力学系
Outline of Final Research Achievements

I proved that, in any dimension greater than one, there are an abelian variety, a smooth rational variety and a Calabi-Yau manifold, with primitive birational automorphisms of first dynamical degree >1. I also proved that there are smooth complex projective Calabi-Yau manifolds and smooth rational manifolds, of any even dimension, with primitive biregular automorphisms of positive topological entropy. As a joint work with Professor Xun Yu, we determined the minimum positive entropy of complex Enriques surface automorphisms.These result give a fairly complete answer to the proposal problems of this grant. Furthermore, as a joint work with Professor Tien-Cuong Dinh, we have shown that there is a smooth complex projective variety, of any dimension greater than or equal to two, whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are mutually non-isomorphic over the real number field.

Academic Significance and Societal Importance of the Research Achievements

当該研究課題の主要部は申請者のICM招待講演において提示した問題の研究であり、十分な成果を得た。まず、高次元代数多様体の力学系理論は低次元理論には帰着できないことを示す定理を確立し、理論の豊かさを示した。Xun Yu氏との共同研究は、フィールズ賞受賞者McMullen氏の結果と合わせることで、複素代数曲面の小平分類の各クラスにおいて正エントロピー値をすべて明らかにする最終的結果である。また、その後、Lesieutre氏の結果に刺激されて行ったDinh氏との共同研究は、当該分野の大家であるDolgachev教授から、長年の未解決問題に対する決定的結果であり、誇ってよい結果であると称賛された。

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • Research Products

    (70 results)

All 2020 2019 2018 2017 2016 2015 Other

All Int'l Joint Research (16 results) Journal Article (23 results) (of which Int'l Joint Research: 11 results,  Peer Reviewed: 21 results,  Acknowledgement Compliant: 11 results) Presentation (19 results) (of which Int'l Joint Research: 19 results,  Invited: 19 results) Funded Workshop (12 results)

  • [Int'l Joint Research] 国立シンガポール大学(シンガポール)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 天津大学(中国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Dusseldorf大学/Bayreuth大学(ドイツ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] KIAS(韓国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 天津大学(中国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Korea Institute for Advanced Study(韓国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Bayreuth 大学(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Singapore 大学(シンガポール)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Natioal University of Singapore(Singapore)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Bayreauth University(Germany)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Hannover University(Germany)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] National University of Singapore(Singapore)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] KIAS/Seoul National University(韓国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Bayreuth U./Berlin Frei U.(Germany)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] KIAS/KIAST(韓国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Rennes(France)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Nef line bundles on Calabi-Yau threefolds, I2020

    • Author(s)
      V. Lazic, K. Oguiso, Th. Peternell
    • Journal Title

      Int. Math. Res. Not.

      Volume: - Issue: 11 Pages: 3498-3526

    • DOI

      10.1093/imrn/rnx191

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Automorphism groups of smooth quintic threefolds2019

    • Author(s)
      K. Oguiso, X. Yu
    • Journal Title

      Asian J. Math.

      Volume: 23

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A few explicit examples of complex dynamics of inertia groups on surfaces--a question of Professor Igor Dolgachev2019

    • Author(s)
      K. Oguiso
    • Journal Title

      Transform. Groups

      Volume: 24

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A surface with discrete and nonfinitely generated automorphism group2019

    • Author(s)
      T.-C. Dinh, K. Oguiso
    • Journal Title

      Duke Math. J.

      Volume: 168

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Pisot units, Salem numbers, and higher dimensional projective manifolds with primitive automorphisms of positive entropy2019

    • Author(s)
      K. Oguiso
    • Journal Title

      Int. Math. Res. Not.

      Volume: 5

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A surface with discrete and non-finitely generated automorphism group2019

    • Author(s)
      T.-C. Dinh, K. Oguiso
    • Journal Title

      Duke Math. J.

      Volume: 168 Issue: 6 Pages: 941966-941966

    • DOI

      10.1215/00127094-2018-0054

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A criterion for the primitivity of a birational automorphism of a Calabi-Yau manifold and an application2018

    • Author(s)
      K. Oguiso
    • Journal Title

      Math. Res. Lett.

      Volume: 25 Pages: 181198-181198

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Morrison-Kawamata cone conjecture and abundance on Ricci flat manifolds2018

    • Author(s)
      V. Lazic, K. Oguiso, Th. Peternell
    • Journal Title

      Adv. Lect. Math. (ALM)

      Volume: 42 Pages: 157185-157185

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A few explicit examples of complex dynamics of inertia groups on surfaces - a question of Professor Igor Dolgachev2018

    • Author(s)
      K. Oguiso
    • Journal Title

      Transformation Group

      Volume: 印刷中 Issue: 2 Pages: 545-561

    • DOI

      10.1007/s00031-018-9473-x

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pisot units, Salem numbers and higher dimensional projective manifolds with primitive automorphisms of positive entropy2017

    • Author(s)
      K. Oguiso
    • Journal Title

      International Mathematics Research Notices

      Volume: 印刷中 Issue: 5 Pages: 13731400-13731400

    • DOI

      10.1093/imrn/rnx142

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Automorphisms of Calabi-Yau threefolds of Picard number three" In: Higher dimensional algebraic geometry - in honour of Professor Yujiro Kawamata's sixtieth birthday2017

    • Author(s)
      V. Lazic, K. Oguiso, Th. Peternell
    • Journal Title

      Adv. Stud. Pure Math

      Volume: 74

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Isomorphic quartic K3 surfaces in the view of Cremona and projective transformations2017

    • Author(s)
      K. Oguiso
    • Journal Title

      In Special Issue for Algebraic Geometry in East Asia, Taiwanese J. Math.

      Volume: 21

    • Related Report
      2017 Annual Research Report
  • [Journal Article] A criterion for the primitivity of a birational automorphism of a Calabi-Yau manifold and an application2017

    • Author(s)
      K. Oguiso
    • Journal Title

      Math. Res. Lett. 印刷中

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Isomorphic quartic K3 surfaces in the view of Cremona and projective transformations2017

    • Author(s)
      K. Oguiso
    • Journal Title

      Taiwanese J. Math. 印刷中

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Automorphisms of elliptic K3 surfaces and Salem numbers of maximal degree2016

    • Author(s)
      H. Esnault, K. Oguiso, X. Yu
    • Journal Title

      Algebraic Geometry

      Volume: 3 Pages: 496-507

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Simple abelian varieties and primitive automorphisms of null entropy of surfaces2016

    • Author(s)
      K. Oguiso
    • Journal Title

      Progress in Math

      Volume: 315 Pages: 279-296

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On automorphisms of the punctual Hilbert schemes of K3 surfaces2016

    • Author(s)
      K. Oguiso
    • Journal Title

      European J. Math.

      Volume: 2 Pages: 246-261

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the unirationality of higher dimensional Ueno-type manifolds2015

    • Author(s)
      F. Catanese, K. Oguiso, A. Verra
    • Journal Title

      Special Issue dedicated to Professor Lucian Badescu on the occasion of 70-th birthday, Romanian Journal of Pure and Applied Mathematics

      Volume: 60 Pages: 337-353

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Non-liftability of automorphism groups of a K3 surface in positive characteristic2015

    • Author(s)
      H. Esnault, K. Oguiso
    • Journal Title

      Math. Ann.

      Volume: 363 Pages: 1187-1206

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Free automorphisms of positive entropy of smooth K\"ahler surfaces2015

    • Author(s)
      K. Oguiso
    • Journal Title

      Adv. Stud. Pure Math.

      Volume: 65 Pages: 187-199

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Some aspects of explicit birational geometry inspired by complex dynamics2015

    • Author(s)
      K. Oguiso
    • Journal Title

      Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures)

      Volume: 2 Pages: 695-721

    • Related Report
      2015 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups2015

    • Author(s)
      S. Cantat, K. Oguiso
    • Journal Title

      Amer. J. Math.

      Volume: 137 Pages: 1013-1044

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Explicit examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy2015

    • Author(s)
      K. Oguiso, T. T. Truong
    • Journal Title

      Kodaira Centennial issue, J. Math. Sci. Univ. Tokyo

      Volume: 22 Pages: 361-385

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Projective rational manifolds with non-finitely generated discrete automorphism group and infinitely many real forms2020

    • Author(s)
      K. Oguiso
    • Organizer
      Complex Dynamics, CIRM, Luminy, France
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Finite generation problem of the discrete automorphism group of a smooth projective variety2019

    • Author(s)
      K. Oguiso
    • Organizer
      Lecture Series in Algebraic Geometry, Morningside Center of Mathematics, Beijing, China.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A surface in odd characteristic with discrete and non-finitely generated automorphism group2019

    • Author(s)
      K. Oguiso
    • Organizer
      the Stefan Banach International Mathematical Center, Warsaw, Poland.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Coble's question and complex dynamics of inertia groups on K3 surfaces2019

    • Author(s)
      K. Oguiso
    • Organizer
      Birational Geometry and Fano varieties dedicated to V. Iskovskikh, Steklov Mathematical Institute, Moscow, Russia
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Inertia Groups, Decomposition Groups and Smooth Projective Varieties with Nonfinite Generated Automorphism Groups2019

    • Author(s)
      K. Oguiso
    • Organizer
      Algebraic, Complex and Arithmetic Dynamics, Simons Symposia, Schloss Elmau, Germany.
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A surface in odd characteristic with discrete and non-finitely generated automorphism group2019

    • Author(s)
      K. Oguiso
    • Organizer
      Higher Dimensional Arithmetic Geometry, Kumamoto
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Smooth complex surfaces with infinitely many real forms2018

    • Author(s)
      K. Oguiso
    • Organizer
      birational geometry and related topics, Shanghai
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Minimum positive entropy of complex Enriques surface automorphisms2018

    • Author(s)
      K. Oguiso
    • Organizer
      Differential, Algebraic and Topological Methods in Complex Algebraic Geometry, Cetraro, Italy
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Smooth complex surfaces with discrete and non -finitely generated automorphism group2018

    • Author(s)
      K. Oguiso
    • Organizer
      Subgroups of Cremona Groups, Oberwolfach
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher dimensional manifolds with primitive birational automorphisms of first dynamical degree >12016

    • Author(s)
      K. Oguiso
    • Organizer
      the Legacy of Emmy Noether and Goettingen Mathematics
    • Place of Presentation
      Yau Mathematical Science Center, Sanya, China
    • Year and Date
      2016-12-19
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher dimensional projective manifolds with primitive automorphisms of positive entropy2016

    • Author(s)
      K. Oguiso
    • Organizer
      International Conference for the 70-th Anniversary of Korean Mathematical Society
    • Place of Presentation
      Seoul National University, Korea
    • Year and Date
      2016-10-23
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On primitive birational automorphisms of odd dimensional2016

    • Author(s)
      K. Oguiso
    • Organizer
      Complex Geometry Conference -- in honor of Ngaiming Mok's 60th birthday--
    • Place of Presentation
      KIAS, Korea.
    • Year and Date
      2016-10-17
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Higher dimensional projective manifolds with primitive automorphisms of positive entropy2016

    • Author(s)
      K. Oguiso
    • Organizer
      Cremona conference
    • Place of Presentation
      Basel, Swissland
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Isomorphic quartic K3 surfaces in the view of Cremona and projective transformations2016

    • Author(s)
      K. Oguiso
    • Organizer
      New methods in birational geometry
    • Place of Presentation
      Toulouse, France
    • Year and Date
      2016-06-27
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Primitive automorphisms, dynamical degrees and relative dynamical degrees (three intensive lectures)2016

    • Author(s)
      K. Oguiso
    • Organizer
      KIAST intensive lectures
    • Place of Presentation
      KAIST, Korea
    • Year and Date
      2016-03-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Primitive automorphisms of projective hyperkaehler 4-folds and Calabi-Yau 4-folds2015

    • Author(s)
      K. Oguiso
    • Organizer
      RIMS Workshop on Complex Dynamics 2015
    • Place of Presentation
      RIMS, Kyoto Japan
    • Year and Date
      2015-12-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Primitive automorphisms of positive entropy of projective hyperkaehler 4-folds and Calabi-Yau 4-folds2015

    • Author(s)
      K. Oguiso
    • Organizer
      Conference on K3 surfaces and related topics
    • Place of Presentation
      KIAS, Seoul, Korea
    • Year and Date
      2015-11-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Primitive automorphisms of positive entropy of projective hyperkaehler 4-folds and Calabi-Yau 4-folds2015

    • Author(s)
      K. Oguiso
    • Organizer
      Workshop on Algebraic Geometry
    • Place of Presentation
      Fudan University, Shanghai, China
    • Year and Date
      2015-10-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Simple abelian varieties and primitive automorphisms of null entropy of surfaces2015

    • Author(s)
      K. Oguiso
    • Organizer
      Workshop in Dynamics and Geometry
    • Place of Presentation
      KIAS, Seoul, Korea
    • Year and Date
      2015-08-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] A few days conference on algebraic geometry, arithmetic and complex dynamics2019

    • Related Report
      2019 Annual Research Report
  • [Funded Workshop] Arithmetic and Algebraic Geometry 20192019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] The 11th Conference on Arithmetic and Algebraic Geometry" (Jan. 22-25, 2018, U. Tokyo)2018

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] Higher dimensional algebraic geometry2018

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] New Trends in Arithmetic and Geometry of2017

    • Place of Presentation
      BIRS, Banff, Canada
    • Year and Date
      2017-03-12
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Higher Dimensional Algebraic Geometry, Holomorphic Dynamics and Their Interactions2017

    • Place of Presentation
      National University of Singapore, Singapore
    • Year and Date
      2017-01-03
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] The 10th Conference on Arithmetic and Algebraic Geometry2016

    • Place of Presentation
      U. Tokyo, Japan
    • Year and Date
      2016-12-12
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] International Conference for the 70th Anniversary of Korean Mathematical Society2016

    • Place of Presentation
      Seoul National University, Korea
    • Year and Date
      2016-10-20
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] RIMS Workshop on Rationality and self-maps of algebraic varieties2016

    • Place of Presentation
      RIMS, Kyoto
    • Year and Date
      2016-06-19
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Arithmetic and Algebraic Geometry 20162016

    • Place of Presentation
      U. Tokyo
    • Year and Date
      2016-01-25
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Algebraic Geometry in East Asia, 20162016

    • Place of Presentation
      U. Tokyo
    • Year and Date
      2016-01-18
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] The 10-th Anniversary Tokyo-Seoul Conference in Mathematics -Algebraic /Arithmetic / Complex Geometry2015

    • Place of Presentation
      U. Tokyo
    • Year and Date
      2015-12-02
    • Related Report
      2015 Annual Research Report

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Published: 2015-04-16   Modified: 2022-11-04  

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