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

17 pages, 4 figures