Mazzeo, Rafe; Swoboda, Jan; Weiss, Hartmut; Witt, Frederik
(2016):
Ends of the moduli space of Higgs bundles.
In: Duke Mathematical Journal, Vol. 165, No. 12: pp. 22272271

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Abstract
We associate to each stable Higgs pair (A(0), Phi(0)) on a compact Riemann surface X a singular limiting configuration (A(infinity), Phi(infinity)), assuming that det Phi has only simple zeroes. We then prove. a desingularization theorem by constructing a family of solutions (A(t), t Phi(t) to Hitchin's equations, which converge to this limiting configuration as t > infinity. 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.