论文标题
关于Meromormormormorphic K-差异的准链贝尔结构的存在
On existence of quasi-Strebel structures for meromorphic k-differentials
论文作者
论文摘要
在本文中，是由在没有边界的紧凑型黎曼表面上的经典概念的概念的动机。事实证明，即使是k的每个差异超过2，在其单数点下满足某些自然条件的每个差异都承认了这种结构。奇数差异的情况大不相同，我们的存在结果涉及一些算术条件。我们讨论了与给定差异相关的一组准螺旋结构，并引入了阳性k差异的子类。最后，我们提供了一个积极理性差异的示例，并解释了它们与多项式系数的线性微分方程理论的经典海因 - 斯泰尔耶斯理论。
In this paper, motivated by the classical notion of a Strebel quadratic differential on a compact Riemann surfaces without boundary we introduce the notion of a quasi-Strebel structure for a meromorphic differential of an arbitrary order. It turns out that every differential of even order k exceeding 2 satisfying certain natural conditions at its singular points admits such a structure. The case of differentials of odd order is quite different and our existence result involves some arithmetic conditions. We discuss the set of quasi-Stebel structures associated to a given differential and introduce the subclass of positive k-differentials. Finally, we provide a family of examples of positive rational differentials and explain their connection with the classical Heine-Stieltjes theory of linear differential equations with polynomial coefficients.
