We prove that the moduli spaces of curves of genus 22 and 23 are of general type. To do
this, we calculate certain virtual divisor classes of small slope associated to linear series of …

We prove a generalisation of the Brill-Noether theorem for the variety of special divisors on a
general curve C of prescribed gonality. Our main theorem gives a closed formula for the …

We consider a general curve of fixed gonality k and genus g. We propose an estimate ρ‾ g, k
(d, r) for the dimension of the variety W dr (C) of special linear series on C, by solving an …

We describe a conjectural stratification of the Brill–Noether variety for general curves of fixed
genus and gonality. As evidence for this conjecture, we show that this Brill–Noether variety …

We show that the non-Archimedean skeleton of the Prym variety associated to an unramified
double cover of an algebraic curve is naturally isomorphic (as a principally polarized tropical …

Splitting type loci are the natural generalizations of Brill-Noether varieties for curves with a
distinguished map to the projective line. We give a tropical proof of a theorem of H. Larson …

We use Young tableaux to compute the dimension of, the Prym–Brill–Noether locus of a
folded chain of loops of any gonality. This tropical result yields a new upper bound on the …

There are several notions of gonality for graphs. The divisorial gonality dgon (G) of a graph
G is the smallest degree of a divisor of positive rank in the sense of Baker–Norine. The …

We draw comparisons between the author's recent construction of limit linear series for
curves not of compact type and the Amini–Baker theory of limit linear series on metrized …

The scramble number of a graph is an invariant recently developed to study chip-firing
games and divisorial gonality. In this paper we introduce the screewidth of a graph, based …