2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149851Let B be a nef and big line bundle on a smooth complex threefold X with canonical bundle K. Let x be a point on X and suppose that BC\ge3 for any curve C passing x, B^2S\ge7 for any surface S containing x, and B^3\ge51. Then K+B is spanned at x. (Ein-Lazarsfeld proved the assertion assuming B^3\ge92.) Corollary: K+3L is spanned if L is an ample line bundle with L^3>1.23 pages, amstexAlgebraic Geometrytext