有理曲线变形虫的棘

L’Enseignement Mathématique Pub Date : 2019-06-11 DOI:10.4171/LEM/65-3/4-3

G. Mikhalkin, Johannes Rau

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引用次数: 2

摘要

对于每一个有理复曲线$C \子集(\mathbf{C}^\times)^n$，我们关联一个有理热带曲线$\Gamma \子集\mathbf{R}^n$，使得$C$的变应虫$\ mathbf{a}(C) \子集\mathbf{R}^n$在$\Gamma$的有界距离内。根据Passare和Rullgard引入的术语，我们称$\Gamma$为$\mathcal{A}(C)$的脊骨。我们用棘来描述有理复曲线序列的热带极限。

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Spines for amoebas of rational curves

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.

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L’Enseignement Mathématique

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