Riemann-Hilbert problem associated to Frobenius manifold structures on Hurwitz spaces: irregular singularity

TL;DR

This paper constructs solutions to Riemann-Hilbert problems with irregular singularities linked to Frobenius manifold structures on Hurwitz spaces, using meromorphic bidifferentials, and explores their interrelations.

Contribution

It provides explicit solutions to complex Riemann-Hilbert problems associated with Frobenius manifolds on Hurwitz spaces, advancing understanding of their structure and interrelations.

Findings

Solutions expressed via meromorphic bidifferentials.

Describes relationships between different Frobenius structures.

Connects Riemann-Hilbert problems to Frobenius manifold deformations.

Abstract

Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The solutions are given in terms of meromorphic bidifferentials defined on the underlying Riemann surface. The relationship between different classes of Frobenius manifold structures on Hurwitz spaces (real doubles, deformations) is described on the level of the corresponding Riemann-Hilbert problems.