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Various problems related to the classification in higher dimensional birational geometry

Research Project

Project/Area Number 25287005
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Algebra
Research InstitutionKyoto University

Principal Investigator

Mori Shigefumi  京都大学, 高等研究院, 特別教授 (00093328)

Research Collaborator Prokhorov Yuri  ステクロフ研究所, 教授
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
KeywordsQコニック束 / 因子収縮射 / フリップ収縮射 / 反標準線形系 / Du Val特異点 / 端末特異点 / Qデルペゾ束 / 極小モデルプログラム / 端収縮射 / フリップ / ファノ多様体
Outline of Final Research Achievements

We study extremal contraction morphisms f to S of a terminal threefold X such that the inverse image F of a point s is a curve, and try to classify the neighbourhood of F especially when F is irreducible. They consist of three kinds, flipping contractions, divisorial contractions, and Q-conic bundles. Among them, flipping contractions were classified, and the other two kinds are studied. There are at most two non-Gorenstein points on F, and the classification of the case of one non-Gorenstein point has been completed.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • Research Products

    (14 results)

All 2017 2016 2015 2014

All Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (12 results) (of which Int'l Joint Research: 10 results,  Invited: 12 results)

  • [Journal Article] Threefold Extremal Contractions of Types (IIA). I2016

    • Author(s)
      S. Mori, Y. Prokhorov
    • Journal Title

      Izvestiya: Mathematics

      Volume: 80 (5) Issue: 5 Pages: 884-909

    • DOI

      10.1070/im8516

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 3-fold extremal contractions of types (IC) and (IIB)2014

    • Author(s)
      Shigefumi Mori, Yuri Prokhorov
    • Journal Title

      Proceedings of the Edinburgh Mathematical Society

      Volume: 57 Issue: 1 Pages: 231-252

    • DOI

      10.1017/s0013091513000850

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] On the classification of algebraic varieties2017

    • Author(s)
      森重文
    • Organizer
      Warwick大学数学談話会
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Extremal contractions of dimension three with fiber dimension 12017

    • Author(s)
      森重文
    • Organizer
      SIMONS CONFERENCE IN MATHEMATICS AND PHYSICAL SCIENCES (BIRATIONAL GEOMETRY)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the classification of algebraic varieties2017

    • Author(s)
      森重文
    • Organizer
      75 Years of Mathematics in Mexico
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the classification of algebraic varieties2017

    • Author(s)
      森重文
    • Organizer
      Kavli IPMU談話会
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational Curves on Algebraic Varieties2016

    • Author(s)
      Shigefumi Mori
    • Organizer
      Benjamin Peirce Centennial Conference
    • Place of Presentation
      Harvard University
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational curves on algebraic varieties2016

    • Author(s)
      Shigefumi Mori
    • Organizer
      Hitchin 70 Conference
    • Place of Presentation
      Math Institute, Oxford University
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational curves on algebraic varieties2016

    • Author(s)
      Shigefumi Mori
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      関西大学
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Rational curves on algebraic varieties2016

    • Author(s)
      Shigefumi Mori
    • Organizer
      韓国数学会70周年記念コンファレンス
    • Place of Presentation
      Seoul National University, Korea
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational Curves on Algebraic Varieties - extremal rays and MMP2015

    • Author(s)
      森 重文
    • Organizer
      12th Congress of the Chinese Mathematical Society
    • Place of Presentation
      Capital Normal University, Beijing
    • Year and Date
      2015-11-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational Curves on Algebraic Varieties - extremal rays and MMP2015

    • Author(s)
      森 重文
    • Organizer
      20th Brazilian Mathematics Colloquium
    • Place of Presentation
      IMPA, Brazil
    • Year and Date
      2015-07-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational Curves on Algebraic Varieties - extremal rays and MMP2015

    • Author(s)
      森 重文
    • Organizer
      the symposium on geometry at Univ. of Macau
    • Place of Presentation
      Univ. of Macau, Macau
    • Year and Date
      2015-05-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 代数多様体の有理曲線についてー極小モデルと端射線ー2015

    • Author(s)
      森 重文
    • Organizer
      第一回早稲田大学数学・応用数理談話会
    • Place of Presentation
      早稲田大学、東京
    • Year and Date
      2015-04-09
    • Related Report
      2015 Annual Research Report
    • Invited

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Published: 2013-05-21   Modified: 2019-07-29  

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