# Spines for amoebas of rational curves

## TL;DR

This paper introduces the concept of spines for amoebas of rational complex curves, linking them to tropical curves and using them to analyze tropical limits of such curves.

## Contribution

It defines spines as rational tropical curves approximating amoebas of rational curves and applies this to study their tropical limits.

## Key findings

- Amoebas of rational curves are close to their spines.
- Spines are rational tropical curves associated with amoebas.
- The method describes tropical limits of rational complex curves.

## Abstract

To every rational complex curve $C \subset (\mathbf{C}^\times)^n$ we associate a rational tropical curve $\Gamma \subset \mathbf{R}^n$ so that the amoeba $\mathcal{A}(C) \subset \mathbf{R}^n$ of $C$ is within a bounded distance from $\Gamma$. In accordance with the terminology introduced by Passare and Rullg{\aa}rd, we call $\Gamma$ the spine of $\mathcal{A}(C)$. We use spines to describe tropical limits of sequences of rational complex curves.