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配备弗罗贝尼乌斯流形的结构。对于属零（其中映射是有理函数）和属一（其中映射是椭圆函数），此结构已明确构造。对于更高的属，存在结果是已知的，但尚未构建明确的解决方案。该项目旨在通过使用肖特基-克莱因素数函数显式地构造全纯映射来纠正这一问题，借鉴了 Strachan 最近的工作（属 1 解决方案）以及 Crowdy 的工作，后者使用肖特基-克莱因素数函数来解决更高阶的问题属势理论问题。