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

Abstract

A. Girand has constructed an explicit two-parameter family of flat connections over the complex projective plane ${\mathbb{P}}^2$. These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a conic and three tangent lines. In this paper, we give a generalization of this construction. That is, we construct an explicit $n$-parameter family of flat connections over the complex projective space ${\mathbb{P}}^n$. Moreover, we discuss the relation between these connections and the Garnier system.

21 pages, 2 figures