Jacobian varieties of reduced tropical curves

TL;DR

This paper investigates the Jacobian varieties of reduced tropical curves in , demonstrating that when the bunch of the curve is a bouquet, the Jacobian forms a higher-dimensional torus, enriching tropical geometric understanding.

Contribution

It establishes a connection between the bunch structure of tropical curves and the topology of their Jacobian varieties, specifically when the bunch is a bouquet.

Findings

Jacobian of a tropical curve with a bouquet bunch is a higher-dimensional torus.

Provides a new perspective on the structure of tropical Jacobians.

Enhances the analogy between tropical and algebraic geometry.

Abstract

On tropical geometry in $\rr^2$, the divisor and the Jacobian variety are defined in analogy to algebraic geometry. For study of these objects, it is important to think of the `bunch' of a tropical curve. In this paper, we will show that if the bunch is a bouquet, then the Jacobian is a higher-dimensional torus.