English

Maximal Brill-Noether loci via K3 surfaces

Algebraic Geometry 2023-06-30 v4

Abstract

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.

Keywords

Cite

@article{arxiv.2206.04610,
  title  = {Maximal Brill-Noether loci via K3 surfaces},
  author = {Asher Auel and Richard Haburcak},
  journal= {arXiv preprint arXiv:2206.04610},
  year   = {2023}
}

Comments

34 pages, 1 figure. Comments welcome

R2 v1 2026-06-24T11:45:24.978Z