2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169003We study families of curves covering a projective surface and give lower bounds on the self-intersection of the members of such families, improving results of Ein-Lazarsfeld and Xu. We apply the obtained inequalities to get new insights on Seshadri constants and geometry of surfaces.8 pagesAlgebraic Geometry14C20; 14D06text