论文标题
$ \ mathbb r^n $中热带曲线功能的本地功能理论
Local theory of functions on tropical curves in $\mathbb R^n$
论文作者
论文摘要
我们首先在热带laurent多项式定义的$ \ mathbb r^n $上开发了局部功能理论。我们研究了函数半度的结构，其中两个函数在固定点的邻居上重合时会确定两个函数。我们看到，这种半序与布尔·劳伦（Boolean Laurent）多项式定义的函数的半度密切相关。然后，我们在热带曲线上发展局部功能理论。我们从一维热带风扇类别构建了一个违反函数到某些半态的类别。作为一个应用程序，我们讨论了起源于一维热带风扇的平滑度。
We first develop the local theory of functions on $\mathbb R^n$ defined by tropical Laurent polynomials. We study the structure of the semiring of functions, where two functions are identified when they coincide on a neighborhood of a fixed point. We see that this semiring is closely related to the semiring of functions defined by Boolean Laurent polynomials. Then we develop the local theory of functions on tropical curves. We construct a contravariant functor from the category of 1-dimensional tropical fans to the category of certain homomorphisms of semirings. As an application, we discuss about the smoothness of 1-dimensional tropical fans at the origin.
