Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities

TL;DR

This paper investigates the Riemann-Hilbert problem related to Frobenius structures on Hurwitz spaces, providing explicit solutions, analyzing the monodromy group, and computing monodromy matrices for specific cases.

Contribution

It offers a new explicit integral-based solution to the Riemann-Hilbert problem for Hurwitz Frobenius manifolds and analyzes their monodromy properties.

Findings

Explicit integral solutions for the Riemann-Hilbert problem.

Detailed analysis of the monodromy group.

Explicit computation of monodromy matrices in special cases.

Abstract

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