2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150326We construct examples of smooth surfaces S in P^6 with no trisecant lines. This list includes examples of surfaces not cut out by quadrics. We prove that unless S has a finite number of disjoint $(-1)$-lines, and each one meets some other line L on the surface with L^2\leq -2, and S is not an inner projection from P^7 the surface belongs to the list of examples.21 pages, DVI file available at http://www.math.kth.se/~sandra/Welcome Mittag-Leffler Report No 13, 1996/97 LatexAlgebraic Geometrytext