2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59777We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or Enriques surface to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big line bundle on a K3 surface to be birationally k-very ample and birationally k-spanned, and relate these concepts to the Clifford index and gonality of smooth curves in |L|.23 pages, 0 figures, slightly improved version (Section 4), added references, to appear in Manuscr. MathAlgebraic Geometry14J28text