Invariants of Singularities with Group Actions

群动作的奇点不变量

• 批准号: 233308117
• 负责人: Professor Dr. Wolfgang Ebeling
• 金额: --
• 依托单位: Institut für Algebraische Geometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/233308117?language=en
• 关键词: Invariants; Singularities; Group; Actions

Indices of vector fields, in particular on singular (real or complex) varieties, have been subject to intensive investigations. The applicant and S.M.Gusein-Zade also contributed to this research. In particular, they suggested considering also indices of 1-forms and of collections of 1-forms or vector fields on singular varieties. The applicant and Gusein-Zade have also studied other invariants like Poincaré series and monodromy zeta functions of complex singularities. In joint work of the applicant with A.Takahashi and later with Gusein-Zade, it turned out that it is important to study singularities together with their groups of symmetries to get among other things a better understanding of duality phenomena. Therefore the main objective of this project is to explore these invariants in the presence of the action of a finite group on the variety. This means to some extent pioneering work. It is planned to study both equivariant and orbifold analogues of the notions and statements. One of the aims is also to apply the results to orbifold Landau-Ginzburg models.

指数的向量场，特别是奇异（真实的或复杂的）品种，已受到深入的调查。申请人和S.M.Gusein-Zade也为这项研究做出了贡献。特别是，他们建议也考虑指数的1-形式和集合的1-形式或向量场的奇异品种。申请人和Gusein-Zade还研究了其他不变量，如庞加莱级数和复奇点的单值zeta函数。在申请人与A.Takahashi以及后来与Gusein-Zade的联合工作中，事实证明，研究奇点及其对称群对于更好地理解对偶现象是很重要的。因此，这个项目的主要目标是探索这些不变量在有限群的作用下的多样性。这在某种程度上是一种开拓性的工作。计划研究这些概念和陈述的等变和轨道类似物。的目的之一也是将结果应用到orbifold Landau-Ginzburg模型。