Moduli of Very Ample Line Bundles

Brian Nugent

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arXiv · 2405.17689

Moduli of Very Ample Line Bundles

Brian Nugent

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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.

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Brian Nugent. 2024-05-27. Moduli of Very Ample Line Bundles. https://arxiv.org/abs/2405.17689

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