Schottky Groups and the construction of higher genus Frobenius manifolds

肖特基群和更高属的弗罗贝尼乌斯流形的构造

• 批准号: 2750785
• 金额: --
• 依托单位: University of Glasgow
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2750785
• 关键词: Schottky; Groups; construction; higher; genus

The moduli space of holomorphic maps from a Riemann surface to the sphere can be equipped with the structure of a Frobenius Manifold. For genus zero (where the maps are rational) and genus one (where the maps are elliptic functions) this structure has been constructed explicitly. For higher genus, existence results are known, but no explicit solutions have been constructed. The project aims to rectify this by using the Schottky-Klein prime function to construct the holomorphic maps explicitly, drawing on recent work of Strachan (genus 1 solutions) and also work of Crowdy who has used the Schottky-Klein prime function to solve higher-genus potential theory problems.

从黎曼曲面到球面的全纯映射的模空间可以具有Frobenius流形的结构。对于亏格零（其中映射是有理数）和亏格一（其中映射是椭圆函数），该结构已被显式构造。对于更高的亏格，存在性结果是已知的，但没有显式的解决方案已经构造。该项目的目的是纠正这一点，使用的肖特基-克莱因素函数来构建全纯映射明确，借鉴最近的工作斯特拉坎（属1的解决方案），也工作的克劳迪谁使用的肖特基-克莱因素函数，以解决更高的属潜在的理论问题。