Computation of some moduli spaces of covers and explicit
$\mathcal S_n$ and $\mathcal A_n$ regular $\QQ (T)$ extensions
with totally real fibers
Abstract. We study the arithmetic of a moduli space parameterizing a
family of covers of $\mathbb P^1$. Our study leads to the computation of
the universal curve associated to our family. We obtain this way explicit
regular realizations of $\mathcal{S}_n$ and $\mathcal{A}_n$-extensions
of $\QQ(x)$ with an interval of totally real fibers.