Isomorphisms between moduli of parabolic Higgs bundles

TL;DR

This paper explores isomorphisms between different moduli spaces of parabolic Higgs bundles using Fourier-Mukai transforms, providing insights into their geometric structures and Hitchin fibrations.

Contribution

It introduces new isomorphisms between moduli problems of parabolic Higgs bundles via Fourier-Mukai transforms, enriching the understanding of their geometric relationships.

Findings

Established isomorphisms between four families of moduli spaces

Demonstrated the use of Fourier-Mukai transforms on spectral curves

Enhanced understanding of Hitchin map examples

Abstract

In this paper we study four families of moduli problems which give rise to two dimensional examples of the Hitchin map. Using a few Fourier-Mukai transforms on the corresponding spectral curves, we give isomorphisms between these moduli problems.