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

By T. Graber, J. Harris, J. Starr. 2002

46 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5bcdaa0a58184e6521a545013e6e2cb126efcc63

Citations in the corpus

• Families of rationally connected varieties (2001, unknown): “It is true, however, if we restrict ourselves to the case g h,d (that is, we have a large number of branch points) and look only at covers whose monodromy is the full symmetric group Sd, [ GHS , Theorem 1]. Given this fact, and observing that our second construction allows us to increase the number ”