Research on Complex Analytic Geometry and Singularity Theory

复解析几何与奇异性理论研究

基本信息

  • 批准号:
    02452001
  • 负责人:
  • 金额:
    $ 4.29万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for General Scientific Research (B)
  • 财政年份:
    1990
  • 资助国家:
    日本
  • 起止时间:
    1990 至 1991
  • 项目状态:
    已结题

项目摘要

The head investigators and the investigators did research in Complex Analytic Geometry and Singularity Theory. Especially, on the research of the singularities of complex analytic foliations which was proposed in the research plans for this project, a survey article was written summarizing the results on the unfolding theory, the determinacy problem, the structure of the singular set and the invariants associated to it which have been obtained mainly by the head investigator. This was presented at the College on Singularity Theory held in Trieste, Italy during the summer of 1991. Also, as to the invariants associated to the singular set, the Baum-Bott residues and the newly found Lehmann residues are studied and the fundamental principle underlying the appearance of these invariants is clarified and some generalizations of them are considered. As to the application of the D-module theory, which was proposed in the previous year, the investigations of the characteristic variety and the … More local structure of the-solution complex of the D-module associated to a complex analytic singular foliation and their relation with the aforementioned invariants are continued.Besides the collaboration of the above research, each of the investigators did research on his own subject as well and obtained many results on the-following subject :Holonomy groupoids for generalized foliations and the Chern-Simons-Maslov classes for symplectic boundles (Suzuki), applications of the singularity theory to the theory of differential equations, especially study of systems of completely integrable first order differential equations (Izumiya), singularity which appear in the projective geometry of curves and the maslov classes of Lagrangian varieties (Ishikawa), the microlocal analysis and its applications, especially the Morse inequality for R-constructible sheaves (Tose), analytic group actions on the complex plane, especially the existence of the separatrix and the proof of the rigidity theorem (Nakai). Less
首席调查员和调查员在复解析几何和奇点理论方面进行了研究。特别是,在研究的奇异性的复杂的解析叶理,这是在本项目的研究计划中提出的,写了一篇综述文章总结的结果展开理论,确定性问题,结构的奇异集和不变量已获得主要由首席研究员。这是提出了在奇点理论学院举行的里雅斯特,意大利在1991年夏天。此外,对于与奇异集相关的不变量,本文还研究了Baum-Bott剩余和新发现的Lehmann剩余,阐明了这些不变量出现的基本原理,并对它们进行了推广。至于去年提出的D模理论的应用,则是对特征品种和 ...更多信息 复解析奇异叶理的D-模的解复形的局部结构及其与上述不变量的关系。除了上述研究的合作外,每个研究者也进行了自己的研究,并在以下主题上获得了许多结果:广义叶理的完整群胚和辛束缚的Chern-Simons-Maslov类(Suzuki),奇异性理论在微分方程理论中的应用,特别是研究完全可积的一阶微分方程组(Izumiya),曲线的射影几何中出现的奇异性和拉格朗日簇的maslov类(石川),微局部分析及其应用,特别是R-可构造层的莫尔斯不等式(Tose),复平面上的解析群作用,特别是分界线的存在性和刚性定理的证明(Nakai)。少

项目成果

期刊论文数量(48)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Nobuyuki Tose: "Morse inequalities for Rーconstructible sheaves" Advances in Math.
Nobuyuki Tose:“R—可构造滑轮的莫尔斯不等式”数学进展。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
Isao Nakai: "Separatrices for conformal transformation groups of C,O" Ann.I'Intst.Fourier.
Isao Nakai:“C、O 的共形变换群的分离”Ann.IIntst.Fourier。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
Goo Ishikawa: "Parametrization of a singular Lagrangian variety" Trans.Amer.Math.Soc.
Goo Ishikawa:“奇异拉格朗日簇的参数化” Trans.Amer.Math.Soc。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
Haruo Suzuki: "ChernーSimonsーMaslov classes in some symplectic vector bundles" Proc.Amer.Math.Soc.
Haruo Suzuki:“某些辛向量丛中的 Chern-Simons-Maslov 类”Proc.Amer.Math.Soc。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
Tatsuo Suwa: "Finite determinacy of analytic foliation germs without formal integrating factors" Proc.Amer.Math.Soc.112. 989-997 (1991)
Tatsuo Suwa:“没有正式积分因子的分析叶芽细菌的有限确定性”Proc.Amer.Math.Soc.112。
  • DOI:
  • 发表时间:
  • 期刊:
  • 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:
    $ 4.29万
  • 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:
    $ 4.29万
  • 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:
    $ 4.29万
  • 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:
    $ 4.29万
  • 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:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Residues on Singular Varieties
单一品种的残留
  • 批准号:
    15340016
  • 财政年份:
    2003
  • 资助金额:
    $ 4.29万
  • 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:
    $ 4.29万
  • 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:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)

相似海外基金

Mathematical innovations woven by singularity theory and geometric topology
奇点理论和几何拓扑编织的数学创新
  • 批准号:
    23H05437
  • 财政年份:
    2023
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (S)
New development of Newton's method in singularity theory
奇点理论中牛顿法的新发展
  • 批准号:
    23K03106
  • 财政年份:
    2023
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Commutative Ring theory using tools of Singularity Theory
使用奇点理论工具的交换环理论
  • 批准号:
    23K03040
  • 财政年份:
    2023
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Singularity theory in mixed characteristic and its applications to the theory of F-singularities and birational geometry
混合特性奇异性理论及其在F-奇异性和双有理几何理论中的应用
  • 批准号:
    22H01112
  • 财政年份:
    2022
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Cross-disciplinary fusion of singular phenomena by singularity theory
奇点理论对奇点现象的跨学科融合
  • 批准号:
    22KK0034
  • 财政年份:
    2022
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))
CAREER: New Frontiers for Frobenius, Singularity Theory, Differential Operators, and Local Cohomology
职业生涯:弗罗贝尼乌斯、奇点理论、微分算子和局部上同调的新领域
  • 批准号:
    1945611
  • 财政年份:
    2020
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Continuing Grant
How is singularity theory applied to mathematics such as surface theory
奇点理论如何应用于表面理论等数学
  • 批准号:
    19K03486
  • 财政年份:
    2019
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Developments and Applications of Geometric Singularity Theory
几何奇点理论的发展与应用
  • 批准号:
    19K03458
  • 财政年份:
    2019
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The minimal model theory for higher-dimensional algebraic varieties and singularity theory
高维代数簇的极小模型理论和奇点理论
  • 批准号:
    19J00046
  • 财政年份:
    2019
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for JSPS Fellows
Understanding exotic spheres from the viewpoint of global singularity theory of smooth maps
从光滑映射全局奇点理论的角度理解奇异球体
  • 批准号:
    18F18752
  • 财政年份:
    2018
  • 资助金额:
    $ 4.29万
  • 项目类别:
    Grant-in-Aid for JSPS Fellows
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