标题： 三元和低 genus 的嵌入热带曲线 显示英文标题

标题： Trigonal and embedded tropical curves of low genus

摘要： 在代数几何中，三重曲线总能嵌入到Hirzebruch曲面中。 在热带几何中，三重性的概念没有唯一的对应翻译。 我们关注的是通过存在一个到直线的3次态射来表征，并讨论与可能嵌入到$\mathbb R^2$的关系，这反映了嵌入到Hirzebruch曲面的情况。 我们的结果可分为三部分：对于低 genus 3 和 4 的热带曲线，我们讨论三重态射与对Hirzebruch曲面多边形对偶的嵌入之间的关系，基于关于双椭圆热带曲线和低 genus 曲线嵌入的研究。 我们比较嵌入的障碍与存在到直线的3次态射的障碍。 最后，我们展示了一些例子，其中非光滑的嵌入可以展开以反映到直线的3次态射的某些特征。 显示英文摘要

摘要： In algebraic geometry, trigonal curves can always be embedded into Hirzebruch surfaces. In tropical geometry, the notion of trigonality does not have a unique translation. We focus on the characterization in terms of the existence of a degree 3 morphism to a line, and discuss relations to possible embeddings into $\mathbb R^2$ reflecting an embedding into a Hirzebruch surface. Our results can be divided into three parts: for tropical curves of low genus 3 and 4, we discuss the relation between a trigonal morphism and an embedding dual to the polygon of a Hirzebruch surface, building on works on embeddings of hyperelliptic tropical curves and curves of low genus. We compare obstructions for embeddings with obstructions for the existence of a degree 3 morphism to a line. Finally, we showcase examples where a non-smooth embedding can be unfolded to reflect certain features of a degree 3 morphism to a line.