The Brill-Noether rank of a tropical curve (Q472637)

In this paper, the Brill-Noether rank of tropical curves varying in families is considered. The main result is that this rank varies upper semicontiuously on the moduli space of tropical curves. A specialization lemma relates it to the dimension of the Brill-Noether locus of an algebraic curve, extending the existing results for metric graphs [\textit{C. M. Lim} et al., Int. Math. Res. Not. 2012, No. 23, 5484--5504 (2012; Zbl 1328.14099)]. To deal with sequences of pairs of tropical curves and divisors, a universal Jacobian for divisors on all tropical curves of a fixed combinatorial type is constructed.