2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76836In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give a detailed study of the compactified space, the divisor at infinity and the moduli space itself. In doing so we reprove some assertions of Laumon and Thaddeus on the nilpotent cone.Latex, 25 pages, to appear in Crelle's JournalAlgebraic GeometryDifferential GeometrySymplectic Geometry58D27;14D20text