The Prym variety of a dilated double cover of metric graphs

TL;DR

This paper computes the volume of the tropical Prym variety associated with a harmonic double cover of metric graphs with dilation, revealing its discontinuous behavior under certain deformations.

Contribution

It introduces a method to calculate the volume of tropical Prym varieties for dilated double covers and analyzes their behavior under deformations.

Findings

Volume of tropical Prym varieties can be explicitly calculated.

Discontinuities occur in the Prym variety under specific deformations.

Behavior depends on changes in the dilation subgraph's connected components.

Abstract

We calculate the volume of the tropical Prym variety of a harmonic double cover of metric graphs having non-trivial dilation. We show that the tropical Prym variety behaves discontinuously under deformations of the double cover that change the number of connected components of the dilation subgraph.