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A study on higher dimensional Fano manifolds using the minimal model theory with scaling

Research Project

Project/Area Number 23740028
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionTokai University

Principal Investigator

TSUKIOKA Toru  東海大学, 理学部, 講師 (30508403)

Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywordsファノ多様体 / 代数幾何学
Outline of Final Research Achievements

We studied higher dimensional Fano manifolds using the theory of extremal contractions. We gave examples of Fano manifolds with small contractions and investigated their property. It is known that by the successive blow-up along a curve and a subvariety of codimension 2, we can get projective varieties with small contractions. We have considered Fano manifolds obtained by this construction. The case of blow-ups of the products of projective spaces are studied in detail. On the other hand, we study on the number of irreducible components of exceptional sets of small contractions. In a special case, we obtained a sufficient condition for this number to be one.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (9 results)

All 2015 2014 2013 2012 Other

All Journal Article (2 results) (of which Acknowledgement Compliant: 1 results,  Peer Reviewed: 1 results) Presentation (7 results)

  • [Journal Article] 特殊な双有理射を持つ4次元ファノ多様体(Fano多様体の最近の進展)2014

    • Author(s)
      月岡 透
    • Journal Title

      数理解析研究所講究録

      Volume: 1897

    • NAID

      120005555421

    • Related Report
      2014 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] On the minimal length of extremal rays for Fano fourfolds2012

    • Author(s)
      Toru Tsukioka
    • Journal Title

      Mathematische Zeitschrift

      Volume: 271 Issue: 1-2 Pages: 555-564

    • DOI

      10.1007/s00209-011-0876-9

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Fano manifolds with small contractions2015

    • Author(s)
      Toru Tsukioka
    • Organizer
      Lefschetz Properties
    • Place of Presentation
      ゲッチンゲン大学(ドイツ、ゲッチンゲン)数学研究所
    • Year and Date
      2015-03-13
    • Related Report
      2014 Annual Research Report
  • [Presentation] 小収縮を持つファノ多様体について2015

    • Author(s)
      月岡 透
    • Organizer
      代数幾何シンポジウム2014 in 岐阜
    • Place of Presentation
      大垣ソフトピアジャパンセンタービル(岐阜県)
    • Year and Date
      2015-01-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] Some remark to Fano fourfolds with small contractions2014

    • Author(s)
      Toru Tsukioka
    • Organizer
      The Fourth TKU-KMITL Joint Symposium on Mathematics and Applied Mathematics
    • Place of Presentation
      東海大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 特殊な双有理射を持つ4次元ファノ多様体2013

    • Author(s)
      月岡 透
    • Organizer
      Fano 多様体の最近の進展
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] On Fano 4-folds with special birational contractions2013

    • Author(s)
      Toru Tsukioka
    • Organizer
      One day workshop on Complex Geometry
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Fano varieties and the Hard Lefschetz Theorem2012

    • Author(s)
      Toru Tsukioka
    • Organizer
      Workshop in Hawaii: Aspects of SLP and WLP
    • Place of Presentation
      Tokai International College in Hawaii (アメリカ合衆国)
    • Related Report
      2012 Research-status Report
  • [Presentation] ファノ多様体の端射線の長さと向井予想

    • Author(s)
      月岡 透
    • Organizer
      第11回 可換環論と鏡映群の表現論研究集会
    • Place of Presentation
      東海大学
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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