Homological Mirror Symmetry of Isolated Hypersurface Singularities With Group Actions

群作用下孤立超曲面奇点的同调镜像对称性

• 批准号: 20684003
• 负责人: TAKAHASHI Atsushi
• 金额: $ 10.82万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (A)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20684003/
• 关键词: 幾何学; 代数学; 数理物理学; ミラー対称性; 特異点

Based on the idea of the Mirror symmetry which interchanges the role of the algebra and the geometry, three kinds of triangulated categories are associated to the algebra, the representation theory and the geometry. Looking at some properties of these triangulated categories, we show that the" Arnold' s strange duality" is now naturally understood as a mirror symmetry between orbifold curves and cusp singularities with group action, which is generalized to an infinite series of singularities.

基于镜像对称的思想，将代数与几何的角色互换，将三种三角化范畴与代数、表示理论和几何联系起来。通过观察这些三角化范畴的一些性质，我们证明了“Arnold奇异对偶”现在可以很自然地理解为具有群作用的轨道曲线和尖点奇点之间的镜像对称，并将其推广到无穷多的奇点序列。

项目成果

GW invariants for weighted projective lines mirror dual to simple elliptic singularities

加权射影线的 GW 不变量镜像对偶到简单椭圆奇点

• 发表时间: 2010
• 作者: W.Ebeling ;A.Takahashi;藤野修;Osamu Fujino;A. Takahashi;藤野修;高橋篤史;藤野修;A. Takahashi;藤野修;高橋篤史;藤野修;A. Takahashi;高橋篤史;藤野修;藤野修;A. Takahashi;高橋篤史;Osamu Fujino;A. Takahashi;高橋篤史;A. Takahashi;A.Takahashi;高橋篤史;A. Takahashi;高橋篤史;A. Takahashi;高橋篤史;A. Takahashi;A.Takahashi;高橋篤史;A. Takahashi;高橋篤史;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi

Mirror Symmetry for Hypersurface Singularities

超曲面奇点的镜像对称

• 发表时间: 2010
• 作者: W.Ebeling ;A.Takahashi;藤野修;Osamu Fujino;A. Takahashi;藤野修;高橋篤史;藤野修;A. Takahashi;藤野修;高橋篤史;藤野修;A. Takahashi;高橋篤史;藤野修;藤野修;A. Takahashi;高橋篤史;Osamu Fujino;A. Takahashi;高橋篤史;A. Takahashi;A.Takahashi;高橋篤史;A. Takahashi;高橋篤史;A. Takahashi;高橋篤史;A. Takahashi;A.Takahashi;高橋篤史;A. Takahashi;高橋篤史;Atsushi Takahashi;Atsushi Takahashi;A. Takahashi;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi

Homological Mirror Symmetry of Singularities

奇点的同调镜像对称

• 发表时间: 2009
• 作者: W.Ebeling ;A.Takahashi;藤野修;Osamu Fujino;A. Takahashi;藤野修;高橋篤史;藤野修;A. Takahashi;藤野修;高橋篤史;藤野修;A. Takahashi;高橋篤史;藤野修;藤野修;A. Takahashi;高橋篤史;Osamu Fujino;A. Takahashi;高橋篤史;A. Takahashi;A.Takahashi;高橋篤史;A. Takahashi;高橋篤史;A. Takahashi;高橋篤史;A. Takahashi;A.Takahashi;高橋篤史;A. Takahashi;高橋篤史;Atsushi Takahashi;Atsushi Takahashi;A. Takahashi;Atsushi Takahashi;Atsushi Takahashi;A. Takahashi;A.Takahashi;Atsushi Takahashi;A. Takahashi;Atsushi Takahashi;A. Takahashi
• 通讯作者: A. Takahashi

Categories of Graded Matrix Factorizations for Regular Systems of Weights with e=-1

e=-1 的正则权重系统的分级矩阵分解类别

• 发表时间: 2009
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: H. Kajiura;K. Saito and A. Takahashi
• 通讯作者: K. Saito and A. Takahashi

Mirror Symmetry of orbifold projective lines

轨道投影线的镜像对称

• 发表时间: 2012
• 作者: 国場敦夫;尾角正人;荒川知幸;今野一宏;T. Arakawa;T. Arakawa;Tomoyuki Arakawa;Atsushi Takahashi;Tomoyuki Arakawa;高橋 篤史;Atsushi Takahashi;Atsushi Takahashi;Atsushi Takahashi
• 通讯作者: Atsushi Takahashi