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).

arXiv comment19 pages, 5 figures, the polynomials are contained in an ancillary file

References in corpus (7)

• Numerical calculation of three-point branched covers of the projective line
• The sporadic group J2, Hauptmodul and Belyi map
• Composite Genus One Belyi Maps
• Belyi map for the sporadic group J1
• Explicit Polynomials Having the Higman-Sims Group as Galois Group over Q(t)
• Explicit Belyi maps over Q having almost simple primitive monodromy groups
• Belyi map for the sporadic group J2

Cited by in corpus (2)

• A family of 4-branch-point covers with monodromy group PSL(6,2)
• A one-parameter family of degree 36 polynomials with PSp(6,2) as Galois group over Q(t)