Residues on Singular Varieties

单一品种的残留

基本信息

项目摘要

The head investigator and the others did research on residues on singular varieties. More specifically :1.We developed a theory of residues of Chern classes of vector bundles on singular varieties with respect to collections of sections. We also gave explicit expressions (analytic, algebraic and topological) of the residues at an isolated singular point.2.We introduced the notion of multiplicity for functions on singular varieties and proved a generalization of a formula of Iversen for holomorphic maps onto a Riemann surface.3.In the case of the top Chern class, the Thom class contains local informations and produces analytic., algebraic and topological invariants through the Bochner-Martinelli kernel. We found the "intermediate Thom classes" for other Chern classes.4.In a collaboration with J.-P.Brasselet and J.Seade, we proved a "proportionality theorem" for the local Euler obstruction of 1-forms on singular varieties.5.In a collaboration with F.Bracci, we prove the existence of parabolic curves at a fixed point of a holomorphic self-map of a singular complex surface, as an application of our residue theory. For this, we developed the intersection theory of curves in singular surfaces, using the Grothendieck residues on singular varieties.6.Besides the above, Ito obtained important results on the Poincare-Hopf type theorems, Ohmoto on the characteristic classes of algebraic stacks, Oka on the fundamental group of the complement of algebraic curves, Tajima on Milnor and Tjurina numbers, Yokuraon motivic characteristic classes, respectively.
首席调查员和其他人对单一品种上的残留进行了研究。更具体地说:1.我们发展了奇异变种上的向量丛的陈氏类关于截集的剩余理论。2.我们引入了奇异簇上函数的重数的概念,证明了黎曼曲面上全纯映射的Iversen公式的推广.3.对于top Chern类,Thom类包含局部信息,并通过Bochner-Martinelli核产生解析、代数和拓扑不变量.4.与J.-P.Brasselet和J.Seade合作,证明了奇异簇上1-形式的局部Euler阻塞的一个“比例定理”.5.与F.Bracci合作,证明了奇异复曲面的全纯自映射的不动点上抛物曲线的存在性,作为我们剩余理论的一个应用.为此,我们利用奇异变量上的Grothendieck留数发展了奇异曲面上曲线的交理论。6.除此之外,Ito在Poincare-Hopf型定理、Ohmoto关于代数堆栈的特征类、Oka关于代数曲线补的基本群、Tajima关于Milnor和Tjuina数、Yokuraon动机特征类等方面分别得到了重要的结果。

项目成果

期刊论文数量(25)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Classifying singular Legendre curves by contactomorphisms
通过接触同态对奇异勒让德曲线进行分类
  • DOI:
  • 发表时间:
    2004
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Y. Ebihara;Y. Miyoshi;K. Asamura;et al;S.Severmann et al.;G.Ishikawa
  • 通讯作者:
    G.Ishikawa
T.Suwa: "Characteristic classes of singular varieties"Sugaku Expositions, A.M.S.. 16. 153-175 (2003)
T.Suwa:“奇异品种的特征类别”Sugaku Expositions,A.M.S.. 16. 153-175 (2003)
  • DOI:
  • 发表时间:
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    0
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A Poincare-Hopf type theorem for holomorphic one-forms
全纯一型的Poincare-Hopf型定理
  • DOI:
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    0
  • 作者:
    T.Ito;B.Scardua
  • 通讯作者:
    B.Scardua
Supersingular K3 surfaces in odd characteristic and sextic double plane
奇特征和六重双平面中的超奇异 K3 表面
  • DOI:
  • 发表时间:
    2004
  • 期刊:
  • 影响因子:
    0
  • 作者:
    大本 亨;T.Ohmoto;諏訪 立雄;伊藤 敏和;岡 睦雄;田島 慎一;與倉 昭治;T.Suwa;T.Ito;M.Oka;S.Tajima;S.Yokura;T.Suwa;I.Nakamura;G.Ishikawa;G.Ishikawa;I.Shimada;I.Shimada
  • 通讯作者:
    I.Shimada
I.Shimada: "Fundamental groups of algebraic fiber spaces"Comment.Math.Helu.. 78. 335-362 (2003)
I.Shimada:“代数纤维空间的基本群”评论.Math.Helu.. 78. 335-362 (2003)
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  • 影响因子:
    0
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SUWA Tatsuo其他文献

SUWA Tatsuo的其他文献

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{{ truncateString('SUWA Tatsuo', 18)}}的其他基金

Theory of residues associated with localization of characteristic classes and its applications
与特征类定位相关的残差理论及其应用
  • 批准号:
    16K05116
  • 财政年份:
    2016
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Residue theory on singular varieties and its applications
奇异品种残差理论及其应用
  • 批准号:
    24540060
  • 财政年份:
    2012
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Estimating non-use value of natural environment by using Kuhn Tucker model
利用Kuhn Tucker模型估算自然环境的非使用价值
  • 批准号:
    23710050
  • 财政年份:
    2011
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
Localization theory of Atiyah classes and its applications
Atiyah类定位理论及其应用
  • 批准号:
    21540060
  • 财政年份:
    2009
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Residues on Singular Varieties
单一品种的残留
  • 批准号:
    18340015
  • 财政年份:
    2006
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Research on Characteristic Classes of Singular Varieties
单一品种特征类研究
  • 批准号:
    11440014
  • 财政年份:
    1999
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Research on Complex Analytic Geometry and Singularity Theory
复解析几何与奇异性理论研究
  • 批准号:
    07454011
  • 财政年份:
    1995
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Research on Complex Analytic Geometry and Singularity Theory
复解析几何与奇异性理论研究
  • 批准号:
    02452001
  • 财政年份:
    1990
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for General Scientific Research (B)

相似海外基金

Theory of residues associated with localization of characteristic classes and its applications
与特征类定位相关的残差理论及其应用
  • 批准号:
    16K05116
  • 财政年份:
    2016
  • 资助金额:
    $ 5.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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