Connectivity and simple connectivity of spaces of differentials

微分空间的连通性和简单连通性

• 批准号: 527465281
• 负责人: Professor Dr. Martin Möller
• 金额: --
• 依托单位: Universidad Nacional Autónoma de México (UNAM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/527465281?language=en
• 关键词: Connectivity; simple; connectivity; spaces; differentials

The geometry of moduli spaces of differentials on curves is connected to a number of seemingly distant parts of mathematics, notably to spaces of stability conditions and to torsion point questions on hyperelliptic curves. Our goal is to investigate connectivity questions for strata of these moduli spaces and leaves of certain foliation given by imposing conditions on periods as well as questions about simple connectivity of the covering spaces given by adding Teichmüller markings.

曲线上微分的模空间的几何学与数学中一些看似遥远的部分有关，特别是与稳定性条件的空间和超椭圆曲线上的扭点问题有关。我们的目标是研究这些模空间的层的连通性问题和通过对周期施加条件给出的某些叶理的叶的连通性问题，以及通过添加Teichmüller标记给出的覆盖空间的简单连通性问题。