Skeletons of Prym varieties and Brill–Noether theory

We show that the non-Archimedean skeleton of Prym variety associated to an unramified double cover algebraic curve is naturally isomorphic (as a principally polarized tropical abelian variety) cover. This confirms conjecture by Jensen and first author. prove new upper bound on dimension Prym-Brill-Noether locus for generic covers curves with fixed even gonality base. Our methods also give proof classical Theorem originally due Welters Bertram.