On a Zeuthen-type problem

Abstract

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

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• Formulae for calculating Hurwitz numbers