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arXiv · 2404.15066

Maximal Brill-Noether loci via degenerations and double covers

Andrei Bud·Richard Haburcak
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Abstract

Using limit linear series on chains of curves, we show that closures of certain Brill--Noether loci contain a product of pointed Brill--Noether loci of small codimension. As a result, we obtain new non-containments of Brill--Noether loci, in particular that all dimensionally expected non-containments hold for expected maximal Brill--Noether loci. Using these degenerations, we also give a new proof that Brill--Noether loci with expected codimension $-\rho\leq \lceil g/2\rceil$ have a component of the expected dimension. Additionally, we obtain new non-containments of Brill--Noether loci by considering the locus of the source curves of unramified double covers.

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Andrei Bud, Richard Haburcak. 2024-04-23. Maximal Brill-Noether loci via degenerations and double covers. https://arxiv.org/abs/2404.15066

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