# Skeletons of Prym varieties and Brill--Noether theory

## TL;DR

This paper establishes a natural isomorphism between the non-Archimedean skeleton of Prym varieties and tropical Prym varieties, confirming a conjecture and providing new bounds and proofs in Prym-Brill-Noether theory.

## Contribution

It proves the conjecture that the skeleton of Prym varieties matches tropical Prym varieties and introduces new bounds and proofs in Prym-Brill-Noether theory.

## Key findings

- Confirmed the isomorphism between skeletons and tropical Prym varieties.
- Provided a new upper bound on the Prym-Brill-Noether locus dimension.
- Offered a new proof of the classical Prym-Brill-Noether Theorem.

## Abstract

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 generic 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.