Tropical intersection products on smooth varieties
Tropical intersection products on smooth varieties
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光滑品种的热带交汇产品
DOI：
10.4171/jems/297
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Lars Allermann
中科院分区：
文献类型：
--
作者：
Lars Allermann
类似于ARXIV：0709.3705的第9章，我们定义了热带线性空间上的热带气旋的交积L^n_k，即在类型为max{0，x_1，…，x_n}^(n-k)*R^n的热带扇面上的热带气旋的交积，然后利用这一结果得到了每一个光滑热带簇上的热带气旋的交积，即由粘合这类热带线性空间产生的每一个热带气旋的交积。与经典代数几何不同，这些乘积总是产生定义明确的循环，而不仅仅是循环类。利用这些交积，我们能够定义沿光滑热带变种之间的态射的热带环流的拉回。在本文中，我们坚持使用arxiv：0709.3705中引入的定义、概念和概念。
In analogy to chapter 9 of arXiv:0709.3705 we define an intersection product of tropical cycles on tropical linear spaces L^n_k, i.e. on tropical fans of the type max{0,x_1,...,x_n}^(n-k)*R^n. Afterwards we use this result to obtain an intersection product of cycles on every smooth tropical variety, i.e. on every tropical variety that arises from gluing such tropical linear spaces. In contrast to classical algebraic geometry these products always yield well-defined cycles, not cycle classes only. Using these intersection products we are able to define the pull-back of a tropical cycle along a morphism between smooth tropical varieties. In the present article we stick to the definitions, notions and concepts introduced in arXiv:0709.3705.