2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66203We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves on projective manifolds.8 pages. to appear on Manuscripta MathematicaAlgebraic Geometry14E30, 14J40, 14J45text