Ends of the moduli space of Higgs bundles

Abstract

We associate to each stable Higgs pair $(A_0,{\Phi }_0)$ on a compact Riemann surface $X$ a singular limiting configuration $(A_{\infty },{\Phi }_{\infty })$, 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 $t\to \infty$. 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.