%0 Journal Article %A Gallego Rodrigo, Francisco Javier %A Purnaprajna, Bangere P. %T Vanishing theorems and syzygies for K3 surfaces and Fano varieties. %D 2000 %@ 0022-4049 %U https://hdl.handle.net/20.500.14352/57294 %X In this article we prove results concerning the vanishing of Koszul cohomology groups on K3 surfaces and n-dimensional Fano varieties of index n - 2. As an application of these vanishings we obtain results on projective normality and syzygies for K3 surfaces and Fano varieties. %~