2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140695This note studies the structure of the divisorial fixed part of the dualizing sheaf of a 1-connected curve D on a smooth surface S. It is shown that if the divisorial fixed part F of the dualizing sheaf is non empty then it has arithmetic genus<1 and each component of F is a smooth rational curve.7pp., to appear in Archive der MathematikAlgebraic Geometry14C20 (Primary) 14J99, 14H45 (Secondary)text