Moduli of Very Ample Line Bundles

Abstract

Let $X$ be a projective variety over a field. In this paper, we will construct a moduli space 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.