Moduli of Very Ample Line Bundles

2024/05/27 by Nugent, Brian
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.17689

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.

Related

• Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
• Excess dimensions for Brill-Noether schemes of stable vector bundles
• Minimal bundles and fine moduli spaces
• The Brill-Noether Theory of the Moduli Spaces of Sheaves on Surfaces
• Excess dimensions of Brill--Noether schemes of rank two stable bundles