We associate to each stable Higgs pair on a compact Riemann surface a singular limiting configuration , assuming that has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions to Hitchin’s equations, which converge to this limiting configuration as . This provides a new proof, via gluing methods, for elements in the ends of the Higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space.
"Ends of the moduli space of Higgs bundles." Duke Math. J. 165 (12) 2227 - 2271, 1 September 2016. https://doi.org/10.1215/00127094-3476914