An analytic construction of the universal moduli space of $\mathrm{SL}_r(\mathbb C)$-Higgs bundles
Year: 2026
Type: preprint
Abstract: We construct the moduli space of marked polystable $\mathrm{SL}_r(\mathbb C)$-Higgs bundles via analytic methods. The resulting space is normal and Hausdorff, and its local models are products of a Teichmüller neighbourhood with a quotient of a quadratic cone. These models preserve the curve parameter and identify the stabilizers. We prove agreement with the complex and unitary gauge-quotient topologies and establish the coarse moduli property for semistable families over reduced analytic bases. The mapping class group and Higgs scaling act holomorphically. Besides, on the stable locus, the moduli spaces that we consider agree with the joint moduli constructed by Collier, Toulisse and Wentworth.
Source: arXiv (Cornell University)
Author: Cao, Shiyu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214077028