First steps in tropical intersection theory
First steps in tropical intersection theory
复制标题
热带交叉理论的第一步
DOI：
10.1007/s00209-009-0483-1
复制
发表时间：
2007
影响因子：
0.8
通讯作者：
Johannes Rau
中科院分区：
文献类型：
--
作者：
Lars Allermann;Johannes Rau
我们建立了热带交叉理论的第一部分。也就是说，我们定义循环、卡地亚除数和这两者之间的交集（不传递到理性等价）并讨论前推和后拉。我们首先为 $${\mathbb{R}^{n}}$$ 中的粉丝执行此操作，然后为本地粉丝的“抽象”周期执行此操作。关于枚举几何中的应用，我们最后看看 $${\mathbb{R}^{n}}$$ 中循环和循环类的有理等价和交积。
We establish first parts of a tropical intersection theory. Namely, we define cycles, Cartier divisors and intersection products between these two (without passing to rational equivalence) and discuss push-forward and pull-back. We do this first for fans in $${\mathbb{R}^{n}}$$ and then for “abstract” cycles that are fans locally. With regard to applications in enumerative geometry, we finally have a look at rational equivalence and intersection products of cycles and cycle classes in $${\mathbb{R}^{n}}$$ .