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 abelian variety) to the tropical Prym variety of the associated tropical double cover. This confirms a conjecture by Jensen and the first author. We prove a new upper bound on the dimension of the Prym–Brill–Noether locus for a generic unramified double cover in a dense open subset in the moduli space of unramified double covers of curves with fixed even gonality on the base. Our methods also give a new proof of the classical Prym–Brill–Noether theorem for generic unramified double covers that is originally due to Welters and Bertram.
"Skeletons of Prym varieties and Brill–Noether theory." Algebra Number Theory 15 (3) 785 - 820, 2021. https://doi.org/10.2140/ant.2021.15.785