On a Zeuthen-type Problem

Abstract

In this paper, we show that every degree $d$ meromorphic function on a smooth connected projective curve $C\subset \PP^2$ of degree $d>4$ is isomorphic to a linear projection from a point $p\in \mathbb {P}^2 \setminus C$ to $\PP^1$. We then pose a Zeuthen-type problem for calculating the plane Hurwitz numbers.