Computation of some Moduli Spaces of covers and explicit S_n and A_n   regular Q(T)-extensions with totally real fibers
  We study and compute an infinite family of Hurwitz spaces parameterizing covers of P_C branched at four points and deduce explicit regular S_n and A_n-extensions over Q(T) with totally real fibers. 
Emmanuel Hallouin and Emmanuel Riboulet-Deyris