Distinguishing Brill-Noether loci

Andreas Leopold Knutsen; Asher Auel; Richard Haburcak

Distinguishing Brill-Noether loci

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arxiv 2406.19993 v1 pith:WRQ7DEHN submitted 2024-06-28 math.AG

Asher Auel , Richard Haburcak , Andreas Leopold Knutsen This is my paper · ORCID

classification math.AG

keywords brill-noetherlocicurvescarryingcertainconjectureconstructdistinguishing

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We construct curves carrying certain special linear series and not others, showing many non-containments between Brill-Noether loci in the moduli space of curves. In particular, we prove the Maximal Brill-Noether Loci conjecture in full generality.

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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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