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5 papers
Brill--Noether loci in genus
Richard Haburcak
A refined Brill--Noether theory seeks to determine which linear series are admitted by a ``general'' curve in a particular Brill--Noether locus. However, as Brill--Noether loci are…
Some reducible and irreducible Brill-Noether loci
Richard Haburcak, Montserrat Teixidor i Bigas
We investigate limit linear series on chains of elliptic curves, giving a simple proof of a conjecture of Farkas stating the existence of curves with a theta-characteristic with a…
Distinguishing Brill-Noether loci
Asher Auel, Richard Haburcak, Andreas Leopold Knutsen
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…
Maximal Brill-Noether loci via degenerations and double covers
Andrei Bud, Richard Haburcak
Using limit linear series on chains of curves, we show that closures of certain Brill--Noether loci contain a product of pointed Brill--Noether loci of small codimension. As a resu…
Maximal Brill--Noether loci via the gonality stratification
Asher Auel, Richard Haburcak, Hannah Larson
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…