Tropical cycles and Chow polytopes
Tropical cycles and Chow polytopes
复制标题
热带循环和 Chow 多胞体
DOI：
10.1007/s13366-012-0122-6
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Alex Fink
中科院分区：
文献类型：
--
作者：
Alex Fink
环面中代数圈的Chow多面体只依赖于它的热带化。推广这一点，我们将一个周多面体与任何抽象的热带品种X在一个tropicalised环面品种：正常的热带超曲面，这周多面体是闵可夫斯基和X和反映骨架的风扇的环面品种。几个重要的多面体与热带品种是特殊情况下，我们的周多面体。我们还表明，周多面体细分不完全区分热带品种的组合类型，并记录证明热带线性空间的两个标准定义的等价性。
The Chow polytope of an algebraic cycle in a torus depends only on its tropicalisation. Generalising this, we associate a Chow polytope to any abstract tropical variety X in a tropicalised toric variety: the normal tropical hypersurface to this Chow polytope is the Minkowski sum of X and a reflected skeleton of the fan of the toric variety. Several significant polyhedra associated to tropical varieties are special cases of our Chow polytope. We show also that Chow polytope subdivisions do not fully distinguish the combinatorial types of tropical variety, and record a proof of the equivalence of two standard definitions of tropical linear spaces.