A new two--parameter family of isomonodromic deformations over the five punctured sphere

The object of this paper is to describe an explicit two–parameter family of logarithmic flat connections over the complex projective plane. These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a circle 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 new algebraic solutions of a Garnier system. Finally, we use the associated Riccati one–forms to construct an interesting non–generic family of transversally projective Lotka–Volterra foliations.