Maximal Brill--Noether loci via the gonality stratification

Author:

Asher Auel, Richard Haburcak, Hannah Larson

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-10-14 16:00:00

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 $\rho=-1,-2$ 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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