原始形式と平坦構造の圏論的構成

原始形式和平面结构的分类构造

• 批准号: 17654015
• 负责人: 齋藤 恭司
• 金额: $ 2.11万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Exploratory Research
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17654015/
• 关键词: 代数学; 幾何学; 数理物理学; ミラー対称性; 数理物理

数理物理学と数学,特にその幾何学の領域において,非可換構造や高次のコホモロジーの役割を要求する目覚しい相互作用が起きているように見える.たとえばミラー対称性をはじめとする弦双対性を説明するには,空間概念の革命的な拡張が必要と思われる.「原始形式の理論」は,「非可換多様体」に対する「周期」の理論であって楕円積分論の自然な拡張となる理論,であると期待される.これは新しい空間概念への一歩となると考えている.本年度も引き続き,特異点理論で80年代中旬に開発された「行列分解」のアイデアを用いて,特異点に対して代数的に定義される導来圏の解析をおこなった.本研究課題の成果は,論文「Categories of graded matrix factorizations for regular systems of weights with $\epsilon=-1$」(arXiv:07080210)(梶浦宏成-齋藤恭司-高橋篤史),論文「Towards categorical construction of Lie algebra」(研究代表者),論文「Weighted Projective Lines Associated to Regular Systems of Weights Dual Type」(arXiv=0711.3907)(研究分担者),などとしてまとめられた.また,RIMS研究集会「Representation Theory of Finite Dimensional Algebras and Lie Theory」およびRIMS研究集会「Categorical Aspects of Algebraic Geometry in Mirror Symmetry」を開催し,国内外の多くの研究者との研究交流を行い,研究成果を発表するとともに多くの知見を得ることができた.

Mathematical Physics: mathematics, especially in the field of science and technology, but it is not possible to make high-order equipment in the field of mathematics, physics, mathematics and physics. It is necessary to think about the revolution in the concept of space. The theory of the original form, the theory of the cycle, the theory of the cycle, the theory of the nature, the theory of the concept of space, the theory of the concept of space, the revolution of the concept of space and the revolution of the concept of space. The new concept of space is an important part of the test. This year, we will introduce the concept of in the middle of this year. In the middle of this year, we will start the analysis of the column and column decomposition of the definition of algebra. The results of this study include "Categories of graded matrix factorizations for regular systems of weights with $\ epsilon=-1 $" (arXiv:07080210), "Towards categorical construction of Lie algebra" (representative of the study), "Weighted Projective Lines Associated to Regular Systems of Weights Dual Type" (arXiv=0711.3907) (the contributor of the study), and "Takeshi Takeshi" (the representative of the research). The RIMS research assembly "Representation Theory of Finite Dimensional Algebras and Lie Theory", the RIMS research assembly "Categorical Aspects of Algebraic Geometry in Mirror Symmetry" has been launched, and many researchers at home and abroad have conducted research exchanges, and the research results have been expressed in the form of information and information.

项目成果

Triangulated categories of graded singularities associated to regular weight systems with e=-1

与 e=-1 的常规权重系统相关的分级奇点的三角剖分类别

• 发表时间: 2007
• 作者: 梶浦宏成;齊藤恭司;高橋篶史;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi;Kyoji Saito;Atsushi Takahashi;Kyoji Saito;Kyoji Saito;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi;Kyoji Saito;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi

Weighted projective hnes associated to regular systems of weights of dual type

与双型权重规则系统相关的加权投影线

• 发表时间: 2007
• 作者: 梶浦宏成;齊藤恭司;高橋篶史;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi;Kyoji Saito;Atsushi Takahashi;Kyoji Saito;Kyoji Saito;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi;Kyoji Saito;Atsushi Takahashi;Kyoji Saito;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi

Homological Mirror Symmetry for Isolated Hypersurface Singularities in one dimension

一维孤立超曲面奇点的同调镜像对称

• 发表时间: 2008
• 作者: 梶浦宏成;齊藤恭司;高橋篶史;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi

Mirror symmetry of weighted-homogeneous isolated hypersurface singularities in two dimensions

二维加权同质孤立超曲面奇点的镜像对称性

• 发表时间: 2007
• 作者: 梶浦宏成;齊藤恭司;高橋篶史;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi;Kyoji Saito;Atsushi Takahashi;Kyoji Saito;Kyoji Saito;Kyoji Saito;Atsushi Takahashi;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi

原始形式と無限次元リー環

原始形式和无限维李代数

• 发表时间: 2008
• 作者: 梶浦宏成;齊藤恭司;高橋篶史;Kyoji Saito
• 通讯作者: Kyoji Saito