A Tropical Intersection Product in Matroidal Fans
A Tropical Intersection Product in Matroidal Fans
复制标题
矩阵扇中的热带交汇产品
DOI：
10.1137/110850141
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Kristin M. Shaw
中科院分区：
文献类型：
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作者：
Kristin M. Shaw
我们构造了拟阵的Bergman扇所包含的热带圈的一个交积。为了做到这一点，我们首先在拟阵理论中的删除和限制操作与Mikhalkin在[Proceedings of the International Congress of Mathematicians，Vol. II，European Mathematical Society，苏黎世，2006，pp. 827- 852]。该乘积推广了Allermann和Rau的乘积[Math.Z.，264（2010），pp. 633- 670]和Allermann [Tropical intersection products on smooth varieties，J. Eur. Math. Soc.（JEMS），14（2012），pp. 107- 126]，并提供了一种不基于与Cartier因子相交的相交循环的替代过程。此外，我们简化的情况下，一维扇圈的二维拟阵扇的定义，并给出了应用的交集产品的热带几何中的可靠性问题。
We construct an intersection product on tropical cycles contained in the Bergman fan of a matroid. To do this we first establish a connection between the operations of deletion and restriction in matroid theory and tropical modifications as defined by Mikhalkin in [Proceedings of the International Congress of Mathematicians, Vol. II, European Mathematical Society, Zurich, 2006, pp. 827--852]. This product generalizes the product of Allermann and Rau [Math. Z., 264 (2010), pp. 633--670] and Allermann [Tropical intersection products on smooth varieties, J. Eur. Math. Soc. (JEMS), 14 (2012), pp. 107--126] and also provides an alternative procedure for intersecting cycles which is not based on intersecting with Cartier divisors. Also, we simplify the definition in the case of one-dimensional fan cycles in two-dimensional matroidal fans and give an application of the intersection product to realiability questions in tropical geometry.