Moduli of Very Ample Line Bundles

Abstract

Let X be a projective variety over a field. In this paper, we will construct a modulispace of very ample line bundles on X. In doing so, we develop a generalization of Fitting ideals to complexes of sheaves on X. We give other applications of these Fitting ideals such as constructing Brill-Noether spaces for higher dimensional varieties and giving a scheme structure to the locus where the projective dimension of a module jumps up.