Tropical fans and the moduli spaces of tropical curves
Tropical fans and the moduli spaces of tropical curves
复制标题
热带扇和热带曲线的模空间
作者：
A. Gathmann;Michael Kerber;H. Markwig
摘要我们给出了热带扇（“热带品种的本地构件”）及其态射的严格定义。对于一个态射的热带风扇相同的尺寸，我们表明，逆图像的数量（计算与适当的热带多重性）的一个点在目标上不依赖于所选择的点;一个声明，可以被看作是一个重要的第一步的热带交叉理论。作为一个应用，我们考虑的有理热带曲线（抽象的和在某些特定的）的模空间与评价和健忘态射。使用我们的结果，这给出了新的，简单的和统一的证明各种热带独立的声明，例如，事实上，通过给定点的有理热带曲线的数量（在任何一个）是独立的点。
Abstract We give a rigorous definition of tropical fans (the ‘local building blocks for tropical varieties’) and their morphisms. For a morphism of tropical fans of the same dimension we show that the number of inverse images (counted with suitable tropical multiplicities) of a point in the target does not depend on the chosen point; a statement that can be viewed as one of the important first steps of tropical intersection theory. As an application we consider the moduli spaces of rational tropical curves (both abstract and in some ℝr) together with the evaluation and forgetful morphisms. Using our results this gives new, easy and unified proofs of various tropical independence statements, e.g. of the fact that the numbers of rational tropical curves (in any ℝr) through given points are independent of the points.