2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79094We study from a geographical point of view fibrations of threefolds over smooth curves, such that the general fibre is of general type. We prove the non-negativity of certain relative invariants under general hypotheses and give lower bounds for the self-interssection of the relative canonical divisor of the fibration, depending on other relative invariants. We also study the influence of the relative irregularity on these bounds. A more detailed study of the lowest cases of the bounds is given.34 pagesAlgebraic Geometrytext