• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

The Picard number of Fano manifolds

Research Project

Project/Area Number 15H06690
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionWaseda University

Principal Investigator

SUZUKI Taku  早稲田大学, 理工学術院, 助教 (60754885)

Project Period (FY) 2015-08-28 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsファノ多様体 / 有理曲線 / ピカール数 / 射影空間 / 収縮射 / 極小有理曲線族 / スロープ安定性 / チャーン指標 / 代数学 / 擬指数 / 端射線収縮射
Outline of Final Research Achievements

For the research task "The Picard number of Fano manifolds", I investigated (1) the Picard number of Fano manifolds in terms of their extremal contractions, (2) higher order minimal families of rational curves associated to Fano manifolds, and (3) slope stability of Fano manifolds. In (1), I proved that Mukai conjecture holds for Fano 6-folds admitting no small contractions. In (2), I introduced higher order minimal families of rational curves associated to Fano manifolds X and a new invariant N(X) as the maximal order of them, and I provided a sufficient condition for Fano manifolds X to have large N(X). In (3), I classified special Fano manifolds with Picard number at most two which are not slope stable

Report

(3 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report

Research Products

(4 results)

All 2017 2016 2015

All Journal Article Presentation

  • [Journal Article] On manifolds swept out by high dimensional hypersurfaces2015

    • Author(s)
      Taku Suzuki
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: 219 Pages: 5394-5401

    • DOI

      10.1016/j.jpaa.2015.05.021

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Higher order minimal families of rational curves and Fano manifolds with nef Chern characters2017

    • Author(s)
      鈴木 拓
    • Organizer
      代数幾何ミニ研究集会
    • Place of Presentation
      埼玉大学
    • Related Report
      2016 Annual Research Report
  • [Presentation] Higher order minimal families of rational curves and Fano manifolds with nef Chern characters2016

    • Author(s)
      鈴木 拓
    • Organizer
      代数幾何学セミナー
    • Place of Presentation
      東京大学
    • Related Report
      2016 Annual Research Report
  • [Presentation] Higher order minimal families of rational curves and Fano manifolds with nef Chern characters2016

    • Author(s)
      鈴木 拓
    • Organizer
      山形代数幾何小研究集会
    • Place of Presentation
      山形大学
    • Related Report
      2016 Annual Research Report

URL: 

Published: 2015-08-26   Modified: 2018-03-22  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi