2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78011Let f:S ->B be a relatively minimal fibred surface. In this note we give a partial affirmative answer to a conjecture of Xiao, proving that the direct image of the relative dualizing sheaf of $f$ is ample when the slope of the fibration is less than 4, if the general fibre of $f$ is non-hyperelliptic or the genus of the fibre or of the base curve is low.2 pages; LatexAlgebraic Geometry14H10, 14J10text