The irreducibility of certain pure-cycle Hurwitz spaces
The irreducibility of certain pure-cycle Hurwitz spaces
We study "pure-cycle" Hurwitz spaces, parametrizing covers of the projective line having only one ramified point over each branch point. We start with the case of genus-$0$ covers, using a combination of limit linear series theory and group theory to show that these spaces are always irreducible. In the case …