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Minimal model program and singularity theory

Research Project

Project/Area Number 16H06710
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionThe University of Tokyo

Principal Investigator

Nakamura Yusuke  東京大学, 大学院数理科学研究科, 助教 (20780034)

Project Period (FY) 2016-08-26 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords極小モデル理論 / ACC予想 / 有理点問題 / LSC予想 / フリップの停止問題 / 特異点 / 極小ログ食い違い係数
Outline of Final Research Achievements

I studied the following two topics: (1)Vanishing theorem of Witt vector cohomology. (2) The ACC conjecture.
(1) As joint work with H. Tanaka, we prove vanishing theorems of
Witt vector coholomogy of Nadel type for 3-dimensional Fano varieties (characteristic > 5). We have two applications. One is the connectedness lemma. Another one is a rational point formula. (2) I study the paper by Birkar on the BAB conjecture, and try to apply the ACC conjecture.

Report

(3 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • Research Products

    (12 results)

All 2018 2017 2016

All Journal Article (1 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 1 results) Presentation (11 results) (of which Int'l Joint Research: 8 results,  Invited: 11 results)

  • [Journal Article] A boundedness conjecture for minimal log discrepancies on a fixed germ2018

    • Author(s)
      M. Mustata, Y. Nakamura
    • Journal Title

      Contemporary Mathematicsに掲載決定

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Vanishing theorems of Witt-vector cohomology for Fano threefolds2018

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Higher dimensional algebraic geometry
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A vanishing theorem of Witt-vector cohomology for Fano threefolds2018

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Algebraic geometry in positive characteristic and related topics
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] A vanishing theorem of Witt-vector cohomology for Fano threefolds2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Classification and Moduli Theory of Algebraic Varieties
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An application of the ACC for LCT'S to the ACC for MLD's2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      NCTS Workshop in Higher Dimensional Algebraic Geometry
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A rational point formula on singular Fano varieties over a finite field2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      BICMR-Tokyo Algebraic Geometry Workshop
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Birkar's paper "Singularities of linear systems and boundedness of Fano varieties" explanation2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      NCTS Workshop on Singularities, Linear Systems, and Fano Varieties
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational points on log Fano threefolds over a finite field2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Workshop on Higher Dimensional Algebraic Geometry, Holomorphic Dynamics and Their Interactions
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] New formulation of the number of rational points on singular Fano varieties over a finite field2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      The 2nd Higher dimensional algebraic geometry Echigo Yuzawa symposium
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Rational points on log Fano threefolds over a finite field2017

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Cambridge--Tokyo Algebraic Geometry workshop 2017
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rational points on log Fano threefolds over a finite field2016

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Tokyo-Princeton algebraic geometry conference, Princeton University
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Birkar's paper "Anti-pluricanonical systems on Fano varieties" explanation2016

    • Author(s)
      Yusuke Nakamura
    • Organizer
      Summer School on Algebraic Geometry
    • Related Report
      2016 Annual Research Report
    • Invited

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Published: 2016-09-02   Modified: 2019-03-29  

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