A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions

Algebraic solutions of the Painlevé VI equation and the Garnier systems have been studied. For example, Girand constructed an explicit two-parameter family of flat connections over the projective plane. These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a conic and three tangent lines. By restricting them to generic lines, we get an algebraic family of isomonodromic deformations of the five-punctured sphere. This yields algebraic solutions of a Garnier system. In this talk, we give a generalization of this construction. That is, we construct an explicit n-parameter family of flat connections over the projective space of dimension n.