Stable intersections of tropical varieties
Stable intersections of tropical varieties
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热带品种的稳定交叉
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Josephine Yu
中科院分区：
文献类型：
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作者：
A. Jensen;Josephine Yu
我们给出了热带周期稳定交叉点的几个特征，并建立了它们的基本属性。我们证明了两个热带品种的稳定交集是经典品种交集经过一般缩放后的热带化。由此得出伯恩斯坦定理的证明。我们证明了热带循环扇的热带交叉环与麦克马伦多面体代数同构。由此可见，每个热带循环扇都是热带超曲面纯幂的线性组合，而这些纯幂总是可以实现的。我们证明由素理想定义的常系数热带品种的每个稳定交集都通过余维一连接。我们还给出了一个可实现的热带品种的例子，它通过余维一连接，但与超平面的稳定交集却不是。
We give several characterizations of stable intersections of tropical cycles and establish their fundamental properties. We prove that the stable intersection of two tropical varieties is the tropicalization of the intersection of the classical varieties after a generic rescaling. A proof of Bernstein’s theorem follows from this. We prove that the tropical intersection ring of tropical cycle fans is isomorphic to McMullen’s polytope algebra. It follows that every tropical cycle fan is a linear combination of pure powers of tropical hypersurfaces, which are always realizable. We prove that every stable intersection of constant coefficient tropical varieties defined by prime ideals is connected through codimension one. We also give an example of a realizable tropical variety that is connected through codimension one but whose stable intersection with a hyperplane is not.