论文标题
用于拉梅功能的模量空间和第二种的阿贝尔积分
Moduli spaces for Lamé functions and Abelian integrals of the second kind
论文作者
论文摘要
阶M的Lamé函数的空间是对成对的空间（椭圆曲线，Abelian差速器）的同构，其中差分在原点上具有2M的单个零零，而M Double Poles具有消失的残基。我们描述了这个空间的拓扑：它是有限类型的黎曼表面；我们发现每个组件的组件数量以及属和欧拉的特征。作为一种应用，我们发现科恩的多项式的程度证实了罗伯特·梅尔（Robert Maier）的猜想。作为另一个应用，我们部分描述了圆锥形奇异性的圆锥形奇异性的球形指标空间的变性基因座，其中圆锥角度为2 $π$的奇数倍数。
The space of Lamé functions of order m is isomorphic to the space of pairs (elliptic curve, Abelian differential) where the differential has a single zero of order 2m at the origin and m double poles with vanishing residues. We describe the topology of this space: it is a Riemann surface of finite type; we find the number of components and the genus and Euler characteristic of each component. As an application we find the degrees of Cohn's polynomials confirming a conjecture by Robert Maier. As another application we partially describe the degeneration locus of the space of spherical metrics on tori with one conic singularity where the conic angle is an odd multiple of 2$π$.
