Maximal Brill-Noether loci via degenerations and double covers

Bud, Andrei; Haburcak, Richard

doi:10.2422/2036-2145.202406_013

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Maximal Brill-Noether loci via degenerations and double covers

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Haburcak, Richard
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2404.15066
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https://doi.org/10.2422/2036-2145.202406_013
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Citation

Bud, A., & Haburcak, R. (in press). Maximal Brill-Noether loci via degenerations and double covers. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, To appear. doi:10.2422/2036-2145.202406_013.

Cite as: https://hdl.handle.net/21.11116/0000-000F-599C-E

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 −ρ≤⌈g/2⌉ 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.