Frobenius manifolds in algebraic geometry and singularity theory

代数几何和奇点理论中的弗罗贝尼乌斯流形

• 批准号: 5416070
• 负责人: Professor Dr. Christian Sevenheck
• 金额: --
• 依托单位: Centre de Mathématiques Laurent Schwartz (CMLS)
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2004-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5416070?language=en
• 关键词: Frobenius; manifolds; algebraic; geometry; singularity

A Frobenius structure on a complex manifold consists of a multiplication on the tangent bundle and a metric subject to several compatibility conditions. These structures appear in quite different branches of mathematics like singularity theory, algebraic topology or differential geometry. Mirror symmetry, one of the central research areas in mathematics and theoretical physics can be stated as equivalence of Frobenius manifolds. The proposal aims at extending the known classes of equivalent Frobenius structures. In particular, we plan to study semi-simple Frobenius manifolds, the Stokes phenomena and quantum cohomology for orbifolds (manifolds modulo finite group actions). We also seek to understand the meaning of structures known in one type of Frobenius manifolds (like gravitational descendants in Gromov-Witten-theory) on the other side of the mirror picture (e.g. in singularity theory).

复流形上的Frobenius结构由切丛上的乘法和满足若干相容条件的度量组成。这些结构出现在非常不同的数学分支，如奇点理论，代数拓扑或微分几何。镜像对称性是数学和理论物理中的一个重要研究领域，它可以看作是Frobenius流形的等价。该建议旨在扩展已知的等价Frobenius结构类。特别是，我们计划研究半简单的Frobenius流形，斯托克斯现象和量子上同调的orbifolds（流形模有限群作用）。我们还试图理解在镜像图像的另一边（例如奇点理论）的一种类型的弗罗贝纽斯流形（就像Gromov-Witten理论中的引力后裔）中已知的结构的意义。