Framed Hitchin Pairs

TL;DR

This paper constructs and analyzes moduli spaces of framed Hitchin pairs, generalizing previous work, removing certain symmetry constraints, and providing a detailed stability analysis without GIT, thus advancing the understanding of these geometric objects.

Contribution

It introduces a unified construction of moduli spaces of framed Hitchin pairs that generalizes prior models and removes symmetry restrictions, with a detailed stability analysis independent of GIT.

Findings

Constructed moduli spaces of framed Hitchin pairs and master spaces.

Removed the symmetry condition ^2G x E -> E = 0 in the construction.

Provided a detailed polynomial stability analysis without GIT.

Abstract

We provide a construction of the moduli spaces of framed Hitchin pairs and their master spaces. These objects have come to interest as algebraic versions of solutions of certain coupled vortex equations by work of Lin and Stupariu. Our method unifies and generalizes constructions of several similar moduli spaces. Here are some points which are also of interest in other similar situations: - Our construction does not require the symmetricity condition that the map ^2G x E -> E be zero, usually appearing in the context of Higgs bundles. - We carry out a detailed analysis of the polynomial stability parameter without referring to GIT. This sheds some light on intrinsic properties of such parameter dependent stability concepts. - The construction corrects an inaccuracy in our previous construction of the compactification of the Hitchin space and generalizes it.