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Studies of families of rational curves and characterizations of homogeneous manifolds

Research Project

Project/Area Number 24840008
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionSaitama 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  Universidad Rey Juan Carlos, KIAS
J. Wiśniewski  Uniwersytet Warszawski
Project Period (FY) 2012-08-31 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsファノ多様体 / ネフ接束 / 等質多様体 / ネフな接束 / 有理曲線
Research Abstract

I have studied Fano manifolds with nef tangent bundles. It is conjectured that such manifolds are rational and homogeneous by Campana and Peternell, which is called the CP conjecture. First, I proved that the conjecture holds for Fano 5-folds of Picard number >1. The result was published from Math Zeitsherift. On the other hand, I studied some problems related to the CP conjecture with R. Munoz, G. Occhetta, L. Sola Conde and J. Wiśniewski. In particular, we proved that Fano manifolds whose elementary contractions are smooth P1-fibrations are complete flag manifolds. As a corollary, the CP conjecture can be boiled down to another problem. We wrote two papers on this topic and these papers are submitted.

Report

(3 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • Research Products

    (33 results)

All 2014 2013 2012 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (29 results) (of which Invited: 10 results) Remarks (1 results)

  • [Journal Article] Fano 5-folds with nef tangent bundles and Picard numbers greater than one2014

    • Author(s)
      K Watanabe
    • Journal Title

      Math. Z.

      Volume: 276, no.1-2 Issue: 1-2 Pages: 39-49

    • DOI

      10.1007/s00209-013-1185-2

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fano 5-folds with nef tangent bundles and Picard numbers greater than one2013

    • Author(s)
      Kiwamu Watanabe
    • Journal Title

      Mathematische Zeitschrift

      Volume: 未定

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On projective manifolds swept out by cubic varieties2012

    • Author(s)
      Kiwamu Watanabe
    • Journal Title

      International Journal of Mathematics

      Volume: (掲載決定) Issue: 07 Pages: 1250058-1250058

    • DOI

      10.1142/s0129167x12500589

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] Characterization of the complete flag manifold of type F42014

    • Author(s)
      渡邉究
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学
    • Year and Date
      2014-03-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2014

    • Author(s)
      渡邉究
    • Place of Presentation
      University of Trento, Italy
    • Year and Date
      2014-02-19
    • Related Report
      2013 Final Research Report
  • [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
      東海大
    • Year and Date
      2014-01-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Characterization of the complete flag manifold of type F42014

    • Author(s)
      渡邉究
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学、東京
    • Related Report
      2013 Annual Research Report
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      渡邉究
    • Organizer
      Algebraic Geometry Seminar
    • Place of Presentation
      名古屋大学
    • Year and Date
      2013-11-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Characterization of complete flag manifolds of classical type2013

    • Author(s)
      渡邉究
    • Organizer
      Japanese-Spanish Workshop
    • Place of Presentation
      Imperial College London, England
    • Year and Date
      2013-07-12
    • Related Report
      2013 Final Research Report
  • [Presentation] On certain manifolds with nef tangent bundle2013

    • Author(s)
      渡邉究
    • Organizer
      A.G.O. FRiDAYS
    • Place of Presentation
      POSTECH, Korea
    • Year and Date
      2013-04-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Fano 5-folds with nef tangent bundles2013

    • Author(s)
      渡邉究
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      渡邉究
    • Organizer
      Recent development of Fano manifolds
    • Place of Presentation
      京都大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      渡邉究
    • Organizer
      Mini workshop on birational geometry
    • Place of Presentation
      東京大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      渡邉究
    • Organizer
      Geometry of Projective Varieties and Related Topics 2013
    • Place of Presentation
      高知大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle2013

    • Author(s)
      渡邉究
    • Organizer
      MSJ Autumn Meeting 2013
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle2013

    • Author(s)
      渡邉究
    • Organizer
      Hodge Theory and Algebraic Geometry
    • Place of Presentation
      東京電機大学
    • Related Report
      2013 Final Research Report
  • [Presentation] Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle2013

    • Author(s)
      渡邉究
    • Organizer
      Hodge Theory and Algebraic Geometry
    • Place of Presentation
      東京電機大学、東京
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle2013

    • Author(s)
      渡邉究
    • Organizer
      MSJ Autumn Meeting 2013
    • Place of Presentation
      愛媛大学、愛媛
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      Kiwamu Watanabe
    • Organizer
      Geometry of Projective Varieties and Related Topics
    • Place of Presentation
      高知大学、高知
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      Kiwamu Watanabe
    • Organizer
      Mini workshop on birational geometry, Univ. of Tokyo.
    • Place of Presentation
      東京大学、東京
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture2013

    • Author(s)
      Kiwamu Watanabe
    • Organizer
      Recent development of Fano manifolds
    • Place of Presentation
      京都大学、京都
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Fano 5-folds with nef tangent bundles2013

    • Author(s)
      渡辺究
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Fano 5-folds with nef tangent bundles and Picard number greater than one2012

    • Author(s)
      渡邉究
    • Organizer
      アフィン代数幾何学研究集会
    • Place of Presentation
      関西学院大学
    • Year and Date
      2012-09-09
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Fano 5-folds with nef tangent bundles and Picard number greater than one2012

    • Author(s)
      渡邉究
    • Place of Presentation
      University of Trento, Italy
    • Year and Date
      2012-08-10
    • Related Report
      2013 Final Research Report
  • [Presentation] Smooth P1-fibrations and Campana-Peternell conjecture2012

    • 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
    • Year and Date
      2012-06-04
    • Related Report
      2013 Final Research Report
  • [Presentation] P1-bundles over projective manifolds and Campana-Peternell conjecture2012

    • Author(s)
      渡邉究
    • Organizer
      都の西北代数幾何学セミナー
    • Place of Presentation
      早稲田大学
    • Year and Date
      2012-05-11
    • Related Report
      2013 Final Research Report
  • [Presentation] P1-bundles over projective manifolds and Campana-Peternell conjecture2012

    • Author(s)
      渡邉究
    • Organizer
      埼玉大学代数幾何講演会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2012-04-25
    • Related Report
      2013 Final Research Report
  • [Presentation] On certain manifolds with nef tangent bundle

    • Author(s)
      Kiwamu Watanabe
    • Organizer
      A.G.O. FRiDAYS
    • Place of Presentation
      POSTECH、Korea
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Characterization of complete flag manifolds of classical type,

    • Author(s)
      Kiwamu Watanabe
    • Organizer
      Japanese-Spanish Workshop
    • Place of Presentation
      Imperial College London、England
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture

    • Author(s)
      渡邉究
    • Organizer
      Algebraic Geometry Seminar, Nagoya Univ.
    • Place of Presentation
      名古屋大学、愛知
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 完全旗多様体の特徴付けとCampana-Peternell予想

    • Author(s)
      渡邉究
    • Organizer
      談話会,東海大
    • Place of Presentation
      東海大学、神奈川
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Characterization of complete flag manifolds and Campana-Peternell conjecture

    • Author(s)
      Kiwamu Watanabe
    • Organizer
      seminar, University of Trento
    • Place of Presentation
      University of Trento、Italy
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Remarks]

    • URL

      http://www.rimath.saitama-u.ac.jp/lab.jp/Kiwamu.Watanabe.html

    • Related Report
      2013 Final Research Report

URL: 

Published: 2012-11-27   Modified: 2019-07-29  

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