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What is commonly meant by Hurwitz's construction of simple covers?

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up vote 3 down vote accepted

I think most people understand under this term the following: It is a branched cover $X\to\mathbb P^1(\mathbb C)$ of a compact connected Riemann surface $X$ to the Riemann sphere $\mathbb P^1(\mathbb C)$ such that the monodromy generators belonging to the branch points are transpositions. Or equivalently: If $n$ is the degree of the cover $f$, then each fiber $f^{-1}(x)$ for $x\in \mathbb P^1(\mathbb C)$ has at least $n-1$ distinct points.

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I don't mind getting a downvote - but still, a short explanation would be fine ... – Peter Mueller Mar 18 '13 at 12:08

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