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Show that a compact Riemann surface admits a branched cover of the sphere with only simple branch points.

I have this problem and it seems to me that the way is to use Riemann Roch theorem, but I do not know how to exactly apply!

Any help is welcome.

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Choose a branch set $D$ of size greater than or equal to the genus. Then by Riemann-Roch, the dimension of the space of meromorphic functions branching on $D$ with at worst simple poles is greater than or equal to $1$.

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