Recognition Problem in Singularity Theory of Differentiable Mappings

可微映射奇异性理论中的识别问题

• 批准号: 14540069
• 负责人: NISHIMURA Takashi
• 金额: $ 2.11万
• 依托单位: Yokohama National University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540069/
• 关键词: Singularity of Differentiable Mapping; Recognition Problem; Mather Theory; International Research; France : Germany; 可微分写像の特異点; ドイツ

Two singularities are said to be equivalent if their local behaviors are essentially same. Though this equibalent relation is very important in "Singularity Theory of Differentiable Mappings", it is quite difficult to give a criterion which is effective in general cases. The problem of giving an effective criterion which works well in general cases is called "Recognition Problem".Before starting this research, the head investor of this research has discovered a new effective method (brief explanation is given in chapter 1) for "Recognition Problem". He has also published many papers on various versions of this new method. The main purpose of this research is to forward a further spread of the above new method. 7.b do so, the head investor adopted the following process of this research.By explaining his new method and adapting it to works (brief explanations are in from chapter 2 to chapter 7) of cooperators who are studying various aspects of "Singularity Theory of Differentiable Mappings", the head investor try to let them comprehend utility of his new method.The head investor also adds a brief explanation of progress on one problem in algebraic geometry from a view point of this research, which he has never noticed when he started this research.

如果两个奇点的局部行为本质上相同，则称它们是等效的。尽管这种等价关系在“可微映射奇异性理论”中非常重要，但给出一个在一般情况下有效的准则是相当困难的。给出一个在一般情况下行之有效的标准的问题被称为“识别问题”。在开始这项研究之前，本研究的首席投资者发现了一种新的有效方法（在第一章中给出了简要解释）“识别问题” ”。他还发表了许多关于这种新方法的各种版本的论文。本研究的主要目的是推动上述新方法的进一步推广。 7.b 为此，首席投资者采用了本研究的以下过程。通过解释他的新方法并将其应用于正在研究“奇点理论”各个方面的合作者的作品（简要说明在第 2 章到第 7 章中） ”，首席投资者试图让他们理解他的新方法的实用性。首席投资者还从本研究的角度对代数几何中的一个问题的进展进行了简要说明，他认为从来没有注意到他什么时候开始这项研究的。

项目成果

西村 尚史: "特異点の数理第2巻 特異点と分岐"共立出版. 408 (2002)

Naoshi Nishimura：“奇点数学第 2 卷奇点和分叉”Kyoritsu Shuppan 408 (2002)。

特異点と分岐

奇点和分岔

• 发表时间: 2002
• 作者: 西村 尚史

Singularities and Bifurcations (in Japanese)

奇点和分岔（日语）

• 发表时间: 2002
• 作者: Nishimura Takashi