Inflection Points of Real and Tropical Plane Curves
Inflection Points of Real and Tropical Plane Curves
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真实和热带平面曲线的拐点
DOI：
10.5427/jsing.2012.4e
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Luc'ia L'opez de Medrano
中科院分区：
文献类型：
--
作者：
Erwan Brugall'e;Luc'ia L'opez de Medrano
我们证明了Viro的拼接产生的真实的代数曲线的最大数量的真实的拐点。特别是这意味着最大的曲折真实的代数$M$-曲线实现许多合痕类型。本文采用的策略是热带的：研究经典平面代数曲线拐点的热带极限。我们用来理解这些热带拐点的主要热带工具是热带修饰。
We prove that Viro's patchworking produces real algebraic curves with the maximal number of real inflection points. In particular this implies that maximally inflected real algebraic $M$-curves realize many isotopy types. The strategy we adopt in this paper is tropical: we study tropical limits of inflection points of classical plane algebraic curves. The main tropical tool we use to understand these tropical inflection points are tropical modifications.