2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73002Let C be an integral projective curve in any characteristic. Given an invertible sheaf L on C of degree 1, form the associated Abel map A_L : C -> P, which maps C into its compactified Jacobian scheme P, and form its pullback map A_L^* : Pic^0_P -> J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, double points, then A_L^* is known to be an isomorphism. We prove that A_L^* always extends to a map between the natural compactifications, Pic^-_P -> P, and that the extended map is an isomorphism if C has, at worst, ordinary nodes and cusps.Plain TeX, 16 pagesAlgebraic Geometry14H40 (Primary) 14K30, 14H20 (Secondary)text