JournalslemVol. 65, No. 3/4pp. 377–396

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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To every rational complex curve C(C×)nC \subset (\mathbb C^\times)^n we associate a rational tropical curve ΓRn\Gamma \subset \mathbb R^n so that the amoeba A(C)Rn\mathcal A(C) \subset \mathbb R^n of CC is within a bounded distance from Γ\Gamma. In accordance with the terminology introduced in [PR], we call Γ\Gamma the spine of A(C)\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 (2019), no. 3/4, pp. 377–396

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