2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150184In this article we prove some strong vanishing theorems on K3 surfaces. As an aplication of them, we obtain higher syzygy results for K3 surfaces and Fano varieties.AMS-TeXAlgebraic Geometry14J10 14J25 (Primary)Vanishing Theorems and Syzygies for K3 Surfaces and Fano Varietiestext