Toric structures in derived categories and representations of algebras

派生范畴中的环面结构和代数表示

• 批准号: 125767185
• 负责人: Privatdozent Dr. Markus Perling
• 金额: --
• 依托单位: Fakultät für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/125767185?language=en
• 关键词: Toric; structures; derived; categories; representations

In this project we want to study relations between algebraic geometry and the representation theory of algebras via tilting theory. The most important aspects we want to investigate are, on the one hand, the construction of so-called exceptional sequences on algebraic varieties, in particular on rational surfaces. On the other hand, for the higher-dimensional case we want to consider relations between tilting theory and birational transforms. A particular role here is played by a paper in superstring theory by Herbst, Hori, and page (2008). The part of this article which is relevant for this project is concerned with the generalization of Landau-Ginzburg models to the multigraded case; in this context, also local aspects of tilting are being investigated. In this project we want to work out and further investigate the mathematical content of these results.

在这个项目中，我们希望通过倾斜理论研究代数几何形状与代数理论之间的关系。一方面，我们要研究的最重要方面是在代数品种上，尤其是在理性表面上构建所谓的特殊序列。另一方面，对于较高维度的情况，我们要考虑倾斜理论与寓言转换之间的关系。 Herbst，Hori和Page（2008）中的一篇论文在SuperString理论中扮演了一个特殊的角色。本文与该项目相关的一部分与Landau-Ginzburg模型的概括为多面案件有关；在这种情况下，也正在研究倾斜的地方方面。在这个项目中，我们希望锻炼并进一步研究这些结果的数学内容。