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Maximal Brill--Noether loci via the gonality stratification

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arxiv 2310.09954 v2 pith:HETMAGQ3 submitted 2023-10-15 math.AG

Asher Auel , Richard Haburcak , Hannah Larson This is my paper · ORCID
classification math.AG
keywords locibrill-noethermaximalconjecturefixedgivegonalitylinear
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abstract

We study the restriction of Brill-Noether loci to the gonality stratification of the moduli space of curves of fixed genus. As an application, we give new proofs that Brill-Noether loci with $\rho=-1$ have distinct support, and for fixed $r$ give lower bounds on when one direction of the non-containments of the Maximal Brill-Noether Loci Conjecture hold for Brill-Noether loci of rank $r$ linear systems. Using these techniques, we also show that Brill-Noether loci corresponding to rank $2$ linear systems are maximal as soon as $g\ge 28$ and prove the Maximal Brill-Noether Loci Conjecture for $g=20$.

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  1. Brill--Noether loci in genus $\leq 12$

    math.AG 2025-07 conditional novelty 7.0 of 10

    For every genus g ≤ 12, the paper identifies exactly which Brill–Noether loci are contained in which, yielding a complete relative-position classification.

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