Generators of invariant linear system on tropical curves for finite isometry group

TL;DR

This paper proves that for a tropical curve with a finite isometry group, the invariant part of the complete linear system associated to an invariant divisor is finitely generated, extending previous work in the field.

Contribution

It extends prior results by demonstrating finite generation of invariant linear systems on tropical curves under finite isometry groups.

Findings

Invariant linear systems are finitely generated under finite isometry groups.

Extension of previous work by Haase, Musiker, and Yu.

Provides a foundation for further algebraic and geometric analysis of tropical curves.

Abstract

For a tropical curve and a finite subgroup of the isometry group of the tropical curve, we prove, extending the work by Haase, Musiker and Yu, that the invariant part of the complete linear system associated to a invariant effective divisor on the tropical curve is finitely generated.