2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61853Let X be a smooth projective complex curve, and let M be the moduli space of stable Higgs bundles on X (with genus g>1), with rank n and fixed determinant ξ, with n and deg(ξ) coprime. Let X' and ξ' be another such curve and line bundle, and M' the corresponding moduli space. We prove that if M and M' are isomorphic as algebraic varieties, then X and X' are isomorphic.LaTeX2e (11 pages)Algebraic Geometry14D20; 14C34text