On Higgs Bundles on Nodal Curves

TL;DR

This paper reviews how generalized parabolic structures help study torsion free sheaves and Hitchin pairs on nodal curves, linking fundamental group representations with moduli spaces and Hitchin maps.

Contribution

It surveys the connections between fundamental group representations and moduli spaces of generalized parabolic bundles and Hitchin pairs on nodal curves.

Findings

Relation between fundamental group representations and moduli spaces.

Construction of an analogue of the Hitchin map for parabolic Hitchin pairs.

Insights into the structure of torsion free sheaves on nodal curves.

Abstract

This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the fundamental group of a nodal curve and the moduli spaces of generalised parabolic bundles and generalised parabolic $L$-twisted Hitchin pairs on its normalisation as well as on an analogue of the Hitchin map for generalised parabolic $L$-twisted Hitchin pairs.