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 $[e,1,\dots ,1]$ with $e\ge 2$.

We were informed that the main theorem had already been proved by Chenakkod, Faraco and Gupta, so we have added this reference and changed the abstract and introduction accordingly