2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58602A line bundle with a base-point-free multiple is called semiample. I give a cohomological characterization of semiample line bundles. The result is a common generalization of the Fujita-Zariski criterion for semiampleness and the Grothendieck-Serre characterization of ampleness. Applying the Fujita-Zariski Theorem, I characterize contractible curves in 1-dimensional families.6 pages. Minor changes. To appear in Kodai Math. JAlgebraic Geometry14A15, 14C20, 14H10text