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

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

2002-05-06

arxiv.org/abs/math/0205056v1

Mathematics

Algebraic Geometry

15 pages, 9 figures

Scientific paper

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.

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