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 (7)

• Irreducibility of Hurwitz spaces
• Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds
• Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)
• Unirationality of Hurwitz spaces of coverings of degree <= 5
• The Hurwitz space of covers of an elliptic curve $E$ and the Severi variety of curves in $E\times {\mathbb{P}}^1$
• Combinatorics of tropical Hurwitz cycles
• Kähler structure on Hurwitz spaces