课题基金 / 基金详情

Commutative ring theory and singularity theory

Commutative ring theory and singularity theory
交换环理论和奇点理论
批准号:
13440015
负责人:
WATANABE Keiichi
金额:
$4.54万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (B)
财政年份:
2001
资助国家:
日本
项目状态:
已结题
起止时间:
2001 至 2004

项目摘要

项目成果

WATANABE Keiichi的其他基金

相关文献

中文摘要
翻译
1.乘子理想;J.Lipman和K.Watanabe证明了二维正则局部环上的每个积分闭理想都是乘子理想;N.Hara和K.Yoshida定义了特征p>0中“紧闭包”的一个推广,并利用这个概念成功地用纯代数方法(用交换环论)计算了乘子理想;S.Takagi和K.Watanabe建立了“F-纯门限”的概念,它对应于特征0中用于代数几何的lc(=对数典范)门限的概念.这一概念在奇点理论和交换环理论中都有许多有趣的特征。2.Hilbert-ukz重数是定义在具有正特征的环上的一种重数。Watanabe和Yoshida以前证明了环是正则的当且仅当环的HK重数为1。这一次我们确定了2维和3维非正则环中HK重数最小的环。
英文摘要
The results are mainly concerning the followings 3 themes1.Multiplier ideals ;J.Lipman and K.Watanabe proved that every integrally closed ideal in 2 dimensional regular local rings is a multiplier ideal.N.Hara and K.Yoshida defined a generalization of "tight closures" in characteristic p>0 and by using that concept, they Succeeded to calculate multiplier ideals by purely algebraic (by commutative ring theory) method.S.Takagi and K.Watanabe established the notion of "F-pure thresholds", which corresponds to the notion of lc(=log canonical) threshold in characteristic 0, used in algebraic geometry. This concept has many interesting features in both singularity theory and commutative ring theory.2.Hilbert-Kunz multiplicity ;Hilbert-Kunz multiplicity is a kind of multiplicity defined for rings of positive characteristics. Watanabe and Yoshida proved before that a ring is regular if and only if the HK multiplicity of the ring is 1. This time we determined the rings whose HK multiplicity is smallest among non-regular rings in dimension 2 and 3.
期刊论文(80)
专著(0)
科研奖励(0)
会议论文
When does the subadditivity theorem for multiplier ideals hold?
乘数理想的次可加性定理何时成立?
DOI: --
发表时间: 2004
期刊: Trans.Amer.Math.Soc. 356
影响因子: --
作者: [K.-i.Watanabe, S.Takagi]
通讯作者: S.Takagi
DOI: 10.1090/s1056-3911-01-00306-x
发表时间: 2000-02
期刊: Journal of Algebraic Geometry
影响因子: 1.8
作者: [Nobuo Hara;Kei-ichi Watanabe]
通讯作者: Nobuo Hara;Kei-ichi Watanabe
DOI: --
发表时间: 2004
期刊: Proceedings of American Mathematical Society 132
影响因子: --
作者: [M.Furuya, M.Tomari]
通讯作者: M.Tomari
N.Hara, K.Watanabe: "F-regular and F-pure rings vs. log terminal and log canonical singularities"J. of Algebraic Geometry. 11. 363-392 (2002)
N.Hara,K.Watanabe:“F-正则环和 F-纯环与对数终端和对数规范奇点”J。
DOI: --
发表时间:
期刊:
影响因子: --
作者: []
通讯作者:
37
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    Revealing the History of Management and Rituals of Sajo-jo Documents in Miyaza Archives: From the Viewpoint of Material Culture
    • 批准号:
      15K16907
    • 项目类别:
      Grant-in-Aid for Young Scientists (B)
    • 资助金额:
      $1.33万
    • 财政年份:
      2015
    • 负责人:
      WATANABE Keiichi
    • 依托单位:
    Commutative Ring Theory of Singularities
    • 批准号:
      26400053
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.66万
    • 财政年份:
      2014
    • 负责人:
      WATANABE Keiichi
    • 依托单位:
    Reconsideration on the Public-service Nature of Japanese Railway Businesses in the Prewar Period
    • 批准号:
      22530348
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.25万
    • 财政年份:
      2010
    • 负责人:
      WATANABE Keiichi
    • 依托单位: