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摘要翻译：
我们给出了热带扇（“热带变种的本地构造块”）及其形态的严格定义。对于同维热带扇的这种形态射，我们证明了目标中一个点的逆像数（用适当的热带倍数计算）不依赖于所选的点--这一陈述可以看作是热带交集理论的开始。作为一个应用，我们考虑了有理热带曲线的模空间（包括抽象的和某些R^R中的模空间）以及求值和遗忘态射。利用我们的结果，这给出了各种热带独立性陈述的新的、简单的和统一的证明，例如，通过给定点的有理热带曲线（在任意r^r中）的数目与点无关的事实。
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英文标题：
《Tropical fans and the moduli spaces of tropical curves》
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作者：
Andreas Gathmann, Michael Kerber, Hannah Markwig
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We give a rigorous definition of tropical fans (the "local building blocks for tropical varieties") and their morphisms. For such 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 the beginning of a tropical intersection theory. As an application we consider the moduli spaces of rational tropical curves (both abstract and in some R^r) 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 R^r) through given points are independent of the points.
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PDF链接：
https://arxiv.org/pdf/0708.2268
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