Zolotarev polynomials of degree 5, 6 and 7 with simple critical points and their moduli spaces

Abstract

A polynomial $p\in \mathbb{C}[z]$ with three finite values is called the Zolotarev polynomial. For a class of such polynomials with the given degree, given passport and simple critical points we define a \emph{combinatorial moduli space}. A combinatorial moduli space have the same essential properties as analytical moduli space, but much easier to construct. We study these objects for Zolotarev polynomials of degree 5, 6 and 7.