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Maximal Brill-Noether loci via K3 surfaces

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arxiv 2206.04610 v4 pith:NCENAHCQ submitted 2022-06-09 math.AG

Asher Auel , Richard Haburcak This is my paper · ORCID
classification math.AG
keywords brill-noetherlocimaximalconjecturecurvesliftinglinearsurfaces
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We explain a strategy for distinguishing Brill-Noether loci in the moduli space of curves by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill-Noether loci with respect to containment. Via an analysis of the stability of Lazarsfeld-Mukai bundles, we obtain new lifting results for linear systems of rank 3 which suffice to prove the maximal Brill-Noether loci conjecture in genus 9-19, 22, and 23.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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.

  2. A remark on the conjecture of Donagi-Morrison

    math.AG 2024-12 conditional novelty 6.0 of 10

    For K3 surfaces, every primitive base point free g^r_d with d≥4, r≥sqrt(d/2), and g>2d-3+(r-1)^2 has a Donagi-Morrison lift N adapted to |C| with Cliff(N⊗O_C)≤Cliff(A).

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