Abstract The Brill–Noether loci M^r₆, ₃ parameterize curves of genus g admitting a linear system of rank r and degree d. When the Brill–Noether number is negative, they are proper subvarieties of the moduli space of genus g curves. We explain a strategy for distinguishing Brill–Noether loci by studying the lifting of linear systems on curves in polarized K3 surfaces, which motivates a conjecture identifying the maximal Brill–Noether loci. Via an analysis of the stability of Lazarsfeld–Mukai bundles, we obtain new lifting results for line bundles of type g^3₃ that suffice to prove the maximal Brill–Noether loci conjecture in genus 3–19, 22, 23, and infinitely many cases.
Auel et al. (Wed,) studied this question.
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