标题： 热带方法到$\mathbb{C}P^3$中的传奇曲线 显示英文标题

标题： Tropical approach to legendrian curves in $\mathbb{C}P^3$

摘要： 著名的扭量构造告诉我们，$S^4$中的调和曲面可以通过$\mathbb{C}P^3$中复数传奇曲线的投影得到。 对后者的热带化的大部分计算尝试进行了介绍。 证明并提出了这些热带曲线的几个组合性质。 提供了在Macaulay2中计算示例的代码。 旅程从绘制通过三个一般点的传奇有理三次曲线开始，并对二次曲面上的传奇曲线进行分类，最后以证明传奇热带曲线的一个组合性质以及使用热带微分形式的第二个性质的启发式论证结束。 显示英文摘要

摘要： The famous twistor construction tells us that harmonic surfaces in $S^4$ can be obtained as projections of complex legendrian curves in $\mathbb{C}P^3$. A mostly computational attempt to study the tropicalizations of the latter curves is presented. Several combinatorial properties of these tropical curves are proven and conjectured. The code in Macaulay2 to compute examples is supplied. The journey starts with drawing a legendrian rational cubics through three generic points and classification of legendrian curves on a quadric surface and ends with a proof of one combinatorial property of legendrian tropical curves and heuristical arguments using tropical differential forms for the second property.