On the Hurwitz existence problem for branched covers of the projective line

Abstract

We give an alternative proof of the Hurwitz existence problem for branched covers of $\mathbb{P}^1$ in the case where the number of ramification points equals the number of branch points, that is, where all the ramification profiles are of the form $[e,1,\ldots,1]$ with $e \geq 2$.