Structural Studies of Fano manifolds with nef tangent bundle

• Project/Area Number: 26800002
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Saitama University
• Principal Investigator: WATANABE Kiwamu 埼玉大学, 理工学研究科, 助教 (20638176)
• Research Collaborator: Muñoz Roberto Universidad Rey Juan Carlos ; Occhetta Gianluca Università di Trento ; Conde Luis E. Solá Università di Trento ; Wiśniewski Jaroslaw A. Uniwersytet Warszawski
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); 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); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: ファノ多様体 / 等質多様体 / 有理曲線 / VMRT / 接朿 / ネフ / 接束 / ネフ接束 / 代数群 / リー環

Outline of Final Research Achievements

I studied characterization problems of homogeneous varieties from the viewpoint of tangent bundle. In particular, I studied the Campana-Peternell conjecture on Fano manifolds with nef tangent bundle (which is the so-called the CP conjecture) and the Mok-Hong-Hwang conjecture on characterizations of homogeneous varieties by these VMRT's (MHH conjecture). I studied these problems with R. Munoz, G. Occhetta, L. E. Sola Conde and J. A. Wisniewski. Seven papers have been published or accepted for publications.

Research Products

• [Int'l Joint Research] University of Trento(Italy)
• [Int'l Joint Research] Trento University(Italy)
• [Journal Article] Low-dimensional projective manifolds with nef tangent bundle in positive characteristic (2017)
  • Author(s): Watanabe, Kiwamu
  • Journal Title: Communications in Algebra Volume: 45 Issue: 9 Pages: 3768-3777
  • DOI: 10.1080/00927872.2016.1245740
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A characterization of symplectic Grassmanianns (2017)
  • Author(s): Occhetta, Gianluca; Sola Conde, Luis E., Watanabe, Kiwamu
  • Journal Title: Mathematische Zeitschrift Volume: 印刷中 Issue: 3-4 Pages: 1421-1433
  • DOI: 10.1007/s00209-016-1807-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Uniform families of minimal rational curves on Fano manifolds (2016)
  • Author(s): Occhetta, Gianluca; Sola Conde, Luis E., Watanabe, Kiwamu
  • Journal Title: Revista Matematica Complutense Volume: 29-2 Issue: 2 Pages: 423-437
  • DOI: 10.1007/s13163-015-0183-9
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle (2015)
  • Author(s): Munoz, Roberto; Occhetta, Gianluca; Sola Conde, Luis E.; Watanabe, Kiwamu
  • Journal Title: Mathematische Annalen Volume: 361 Issue: 3-4 Pages: 583-609
  • DOI: 10.1007/s00208-014-1083-x
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Fano manifolds with nef tangent bundle and large Picard number (2015)
  • Author(s): Watanabe, Kiwamu
  • Journal Title: Proceedings of the Japan Academy, Series A, Mathematical Sciences Volume: 91 Issue: 6 Pages: 89-94
  • DOI: 10.3792/pjaa.91.89
  • NAID: 40020519528
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A survey on the Campana-Peternell Conjecture (2015)
  • Author(s): Munoz, Roberto; Occhetta, Gianluca; Sola Conde, Luis E.; Watanabe, Kiwamu; Wisniewski, Jaroslaw A.
  • Journal Title: Rendiconti dell'Istituto di Matematica dell'Università di Trieste Volume: 47 Pages: 127-185
  • DOI: 10.13137/0049-4704/11223
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Characterizations of rational homogeneous manifolds (2017)
  • Author(s): Watanabe, Kiwamu
  • Organizer: Workshop on Fano varieties and Calami-Yau varieties
  • Place of Presentation: 神戸大学六甲大第二キャンパス（兵庫県神戸市）
  • Year and Date: 2017-01-23
  • Int'l Joint Research / Invited
• [Presentation] Fano manifolds with nef tangent bundle (2016)
  • Author(s): 渡邉究
  • Organizer: 都の西北代数幾何学シンポジウム
  • Place of Presentation: 早稲田大学西早稲田キャンパス（東京都新宿区）
  • Year and Date: 2016-11-18
  • Invited
• [Presentation] A Characterization of Symplectic Grassmanianns (2016)
  • Author(s): 渡邉究
  • Organizer: 代数曲面ワークショップ
  • Place of Presentation: 首都大東京秋葉原サテライトキャンパス（東京都千代田区）
  • Year and Date: 2016-11-12
  • Invited
• [Presentation] Fano manifolds with nef tangent bundle (2016)
  • Author(s): Watanabe, Kiwamu
  • Organizer: International Conference on Spherical Varieties
  • Place of Presentation: （Yau Mathematical Sciences Center（中国、海南島）
  • Year and Date: 2016-11-08
  • Int'l Joint Research / Invited
• [Presentation] A Characterization of Symplectic Grassmanianns (2016)
  • Author(s): 渡邉究
  • Organizer: 日本数学会秋季綜合分科会
  • Place of Presentation: 関西大学千里山キャンパス（大阪府吹田市）
  • Year and Date: 2016-09-19
• [Presentation] A Characterization of Symplectic Grassmanianns (2016)
  • Author(s): 渡邉究
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 九州大学伊都キャンパス（福岡県福岡市）
  • Year and Date: 2016-06-09
  • Invited
• [Presentation] A Characterization of Symplectic Grassmanianns (2016)
  • Author(s): 渡邉究
  • Organizer: 東大数理代数幾何セミナー
  • Place of Presentation: 東京大学駒場キャンパス（東京都目黒区）
  • Year and Date: 2016-05-31
  • Invited
• [Presentation] Fano manifolds with nef tangent bundle (2016)
  • Author(s): 渡邉究
  • Organizer: 第１４回アフィン代数幾何学研究集会
  • Place of Presentation: 関西学院大学大阪梅田キャンパス（ 大阪府、大阪市 ）
  • Year and Date: 2016-03-06
  • Invited
• [Presentation] 等質多様体の紹介と完全旗多様体の特徴付け (2015)
  • Author(s): 渡邉究
  • Organizer: 早稲田大学整数論セミナー
  • Place of Presentation: 早稲田大学西早稲田キャンパス（ 東京都、新宿区 ）
  • Year and Date: 2015-10-09
  • Invited
• [Presentation] Uniform families of minimal rational curves on Fano manifolds (2015)
  • Author(s): 渡邉究
  • Organizer: 日本数学会秋季綜合分科会
  • Place of Presentation: 京都産業大学神山キャンパス（ 京都府、京都市 ）
  • Year and Date: 2015-09-15
• [Presentation] Uniform families of minimal rational curves on Fano manifolds (2015)
  • Author(s): 渡邉究
  • Organizer: 第３回 K3曲面・エンリケス曲面ワークショップ
  • Place of Presentation: 北海道教育大札幌駅前サテライトキャンパス（ 北海道、札幌市 ）
  • Year and Date: 2015-08-17
  • Invited
• [Presentation] Fano manifolds with nef tangent bundle and large Picard number (2015)
  • Author(s): 渡邉究
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学、駿河台キャンパス
  • Year and Date: 2015-03-21
• [Presentation] Fano manifolds with nef tangent bundles (2015)
  • Author(s): Watanabe, Kiwamu
  • Organizer: Mini-conference on Algebraic Geometry
  • Place of Presentation: National Taiwan University、台湾、台北市
  • Year and Date: 2015-03-06
  • Invited
• [Presentation] Fano manifolds with nef tangent bundles (2015)
  • Author(s): 渡邉究
  • Organizer: 代数幾何学セミナー
  • Place of Presentation: 京都大学、理学部数学科
  • Year and Date: 2015-02-06
  • Invited
• [Presentation] Contact structure, dual varieties and Fano manifolds with nef and big tangent bundle (2014)
  • Author(s): 渡邉究
  • Organizer: 代数多様体とその周辺
  • Place of Presentation: 琉球大学、理学部数理科学科
  • Year and Date: 2014-10-02
  • Invited
• [Presentation] 完全旗多様体の特徴付けとCampana-Peternell予想 (2014)
  • Author(s): 渡邉究
  • Organizer: 談話会
  • Place of Presentation: 東京理科大学、理工学部数学科、野田）
  • Year and Date: 2014-05-23
  • Invited
• [Presentation] Characterization of complete flag manifolds (2014)
  • Author(s): 渡邉究
  • Organizer: 特異点月曜セミナー
  • Place of Presentation: 日本大学、文理学部数学科
  • Year and Date: 2014-04-21
  • Invited
• [Remarks] Kiwamu Watanabe
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/Kiwamu.Watanabe.html
• [Remarks]
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/Kiwamu.Watanabe.html
• [Remarks]
  • URL: http://www.rimath.saitama-u.ac.jp/lab.jp/Kiwamu.Watanabe.html