An approach for computing families of multi-branch-point covers and applications for symplectic Galois groups

Abstract

We propose an approach for the computation of multi-parameter families of Galois extensions with prescribed ramification type. More precisely, we combine existing deformation and interpolation techniques with recently developed strong tools for the computation of $3$-point covers. To demonstrate the applicability of our method in relatively large degrees, we compute several families of polynomials with symplectic Galois groups, in particular obtaining the first totally real polynomials with Galois group PSp(6,2).