# Spines for amoebas of rational curves

### Grigory Mikhalkin

Université de Genève, Genève, Switzerland### Johannes Rau

Universidad de los Andes, Bogotá, Colombia

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## Abstract

To every rational complex curve $C \subset (\mathbb C^\times)^n$ we associate a rational tropical curve $\Gamma \subset \mathbb R^n$ so that the amoeba $\mathcal A(C) \subset \mathbb R^n$ of $C$ is within a bounded distance from $\Gamma$. In accordance with the terminology introduced in [PR], we call $\Gamma$ the *spine* of $\mathcal A(C)$. We use spines to describe tropical limits of sequences of rational complex curves.

## Cite this article

Grigory Mikhalkin, Johannes Rau, Spines for amoebas of rational curves. Enseign. Math. 65 (2020), no. 3, pp. 377–396

DOI 10.4171/LEM/65-3/4-3