A note on Hurwitz schemes of covers of a positive genus curve

Abstract

We prove the irreducibility of the space parametrizing branched covers of a fixed Riemann surface $B$ of degree $d$, with at least 2d branch points, and with monodromy group equal to $S_d$. The result is classical for $g(B)=0$. The result is well-known for $g(B)>0$, but we could find no reference.

15 pages, 9 figures

Cited by in corpus (2)

• Irreducibility of Hurwitz spaces
• Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds