论文标题
热带平面曲线中的棱镜图
Prism graphs in tropical plane curves
论文作者
论文摘要
任何光滑的热带平面曲线都包含一个称为其骨骼的杰出三价图。 2020年，莫里森（Morrison）和图瓦里（Tewari）证明，所谓的大面部图不能是$ 12 $及以上的热带曲线的骨架。在本文中，我们回答了一个开放的问题，他们提出了将结果扩展到棱镜图的，证明它们是光滑的热带平面曲线的骨骼，当时该属最多为$ 11 $。我们的主要工具是将晶格多边形的分类分为两个点，而不是同时查看所有其他分类，而没有任何一个可以观察所有其他点的点。
Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton. In 2020 Morrison and Tewari proved that the so-called big face graphs cannot be the skeleta of tropical curves for genus $12$ and greater. In this paper we answer an open question they posed to extend their result to the prism graphs, proving that they are the skeleton of a smooth tropical plane curve precisely when the genus is at most $11$. Our main tool is a classification of lattice polygons with two points than can simultaneously view all others, without having any one point that can observe all others.
