| This is joint work with Rob Lazarsfeld. We study the minimal resolution of the coordinate ring of a smooth projective variety X, when X is embedded into a projective space by a line bundle of the form L^d, where L is a very ample line bundle. We study the behavior of the Koszul cohomologies, as d goes to infinity. We will also discuss the syzygies of the d-Veronese embedding of the projective space. |