On existence of quasi-Strebel structures for meromorphic k-differentials

Autor:	Shapiro, Boris, Tahar, Guillaume
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Geometric Topology Primary 30F30 Secondary 31A05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 tages, 8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.10280 Zobrazit plný text záznamu View this record from Arxiv