RiemannHilbert problem for Hurwitz Frobenius manifolds: Regular singularities

In this paper we study the Fuchsian RiemannHilbert (inverse monodromy) problem corresponding to Frobenius structures on Hurwitz spaces. We find a solution to this RiemannHilbert problem in terms of integrals of certain meromorphic differentials over a basis of an appropriate relative homology space over a Riemann surface, study the corresponding monodromy group and compute the monodromy matrices explicitly for various special cases.