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

Tom Graber·Joe Harris·Jason Starr
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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.

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Tom Graber, Joe Harris, Jason Starr. 2002-05-06. A note on Hurwitz schemes of covers of a positive genus curve. https://arxiv.org/abs/math/0205056

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