论文标题
计算具有交叉比例约束的热带理性空间曲线
Counting tropical rational space curves with cross-ratio constraints
论文作者
论文摘要
这是Arxiv：1805.00115的后续论文，其中列举了满足一般位置点和交叉比率条件的表面的合理曲线。 ARXIV中提供的合适的对应定理：1509.07453使我们能够使用热带几何形状，尤其是一种称为落地图的变性技术。该对应定理也具有更高的维度。 在当前的论文中，我们引入了所谓的交叉比例地板图，并表明它们使我们能够确定满足一般位置点和交叉比率条件的理性空间曲线的数量。此外，引入了图形贡献，它提供了一种新颖的结构化方法，以理解$ \ Mathbb {r}^3 $中的地板分解曲线的多重性。另外，使用热带曲线上的所谓条件流以反映在热带曲线上施加的条件如何产生不同类型的边缘。这个概念适用于任意维度。
This is a follow-up paper of arXiv:1805.00115, where rational curves in surfaces that satisfy general positioned point and cross-ratio conditions were enumerated. A suitable correspondence theorem provided in arXiv:1509.07453 allowed us to use tropical geometry, and, in particular, a degeneration technique called floor diagrams. This correspondence theorem also holds in higher dimension. In the current paper, we introduce so-called cross-ratio floor diagrams and show that they allow us to determine the number of rational space curves that satisfy general positioned point and cross-ratio conditions. Moreover, graphical contributions are introduced which provide a novel and structured way of understanding multiplicities of floor decomposed curves in $\mathbb{R}^3$. Additionally, so-called condition flows on a tropical curve are used to reflect how conditions imposed on a tropical curve yield different types of edges. This concept is applicable in arbitrary dimension.
