Spines for amoebas of rational 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 Rullgard, we call $\Gamma$ the spine of $\mathcal{A}(C)$. We use spines to describe tropical limits of sequences of rational complex curves.