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2008 Fiscal Year Final Research Report

Algebro-Geometric Approach to Invariants in Commutative Algebra

Research Project

  • PDF
Project/Area Number 18540007
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTohoku University

Principal Investigator

HARA Nobuo  Tohoku University, 大学院・理学研究科, 准教授 (90298167)

Co-Investigator(Renkei-kenkyūsha) ISHIDA Masanori  東北大学, 大学院・理学研究科, 教授 (30124548)
OGATA Shoetsu  東北大学, 大学院・理学研究科, 准教授 (90177113)
KAJIWARA Takeshi  横浜国立大学, 大学院・工学研究院, 准教授 (00250663)
Project Period (FY) 2006 – 2008
Keywords代数幾何 / 可換環論 / 特異点 / 正標数 / フロベニウス写像 / F-特異点 / F-純閾値 / F-跳躍数
Research Abstract

正標数の可換環論における不変量や特異点の性質, とくに, F-純閾値, F-跳躍数や強F-正則性などについて, 代数幾何的な手法を用いて研究し, 2次元正則局所環の場合のF-純閾値, F-跳躍数の振る舞いを明らかにした. また, 強F-正則性と対数的端末特異点の対応を従来の仮定(Q-Gorenstein性)より弱い仮定(混標数モデルにおける反標準環の有限生成性)の下で証明した.

  • Research Products

    (7 results)

All 2008 2007 2006

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (6 results)

  • [Journal Article] F-pure thresholds and F-jumping exponents in dimension two, with an appendix by Paul Monsky2006

    • Author(s)
      N. Hara
    • Journal Title

      Mathematical Research Letters 13

      Pages: 747-760

    • Peer Reviewed
  • [Presentation] F-特異点とその応用2008

    • Author(s)
      原伸生
    • Organizer
      玉原代数幾何セミナー2008
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2008-08-11
  • [Presentation] Strong F-regularity vs.log ter-minal singularity in non-Q-Gorenstein case2008

    • Author(s)
      N. Hara
    • Organizer
      Commutative Algebra and its Interactions, A conference in honor of Mel Hochster
    • Place of Presentation
      University of Michigan, USA
    • Year and Date
      2008-08-04
  • [Presentation] Bound for Frobenius destabilized semistable bundles and Harder-Narasi-mhan filtrations in characteristic p(after Langer, Shepherd-Barron et.al.)2007

    • Author(s)
      原伸生
    • Organizer
      代数幾何学都留ワークショップ
    • Place of Presentation
      都留文科大学
    • Year and Date
      2007-09-27
  • [Presentation] Multiplier idealの標数0の手法と標数$p$の手法及びその応用II2006

    • Author(s)
      原伸生
    • Organizer
      短期共同研究集会"Arc Spaces and Multiplier Ideals"
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-08-29
  • [Presentation] Multiplier idealの標数0の手法と標数$p$の手法及びその応用I2006

    • Author(s)
      原伸生
    • Organizer
      短期共同研究集会"Arc Spaces and Multiplier Ideals"
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-08-28
  • [Presentation] Characteristic p method : F-sin- gularities, ARCC Workshop "Numerical Invariants of Singularities and Higher-Dimensional Algebraic Varieties,"2006

    • Author(s)
      N. Hara
    • Organizer
      Ameri-can Institute of Mathematics
    • Place of Presentation
      Palo Alto, USA
    • Year and Date
      2006-08-01

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Published: 2010-06-10   Modified: 2016-04-21  

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