References & Citations
Mathematics > Algebraic Geometry
Title: Maximal Brill-Noether loci via degenerations and double covers
(Submitted on 23 Apr 2024)
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 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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