2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68468In this paper we prove the equivalence of two conjectures on linear systems through fat points on a generic K3 surface. The first conjecture is exactly as Segre conjecture on the projective plane. Whereas the second characterizes such linear system and can be compared to the Gimigliano-Harbourne-Hirschowitz conjecture.8 pages, LaTeXAlgebraic Geometry14C20, 14J28text