Chip-firing games, Jacobians, and Prym varieties

TL;DR

This paper introduces chip-firing games on metric graphs and tropical Prym varieties, exploring their connections to algebraic geometry and proposing future research directions.

Contribution

It provides a self-contained introduction to these topics and discusses their algebraic counterparts, bridging combinatorial and algebraic perspectives.

Findings

Established foundational concepts of chip-firing games and tropical Prym varieties.

Explored connections between tropical and algebraic geometry.

Suggested new directions for research in tropical and algebraic geometry.

Abstract

We present a self-contained introduction to the theory of chip-firing games on metric graphs, as well as the more recent theory of tropical Prym varieties. We briefly discuss the connection between these notions and their algebraic counterparts and suggest various avenues for future research.