论文标题
热带理想的品种平衡
Varieties of Tropical Ideals are Balanced
论文作者
论文摘要
热带理想，在ARXIV中引入：1609.03838，定义了热带感谢您的品种的亚化。我们证明，它们的顶级部分是其与理想相同维度的平衡多面体复合物。这意味着，由热带理想定义的热带复曲面品种的每个亚气管都在福利型品种的食物环中具有相关类别。证明的关键工具是，在热带理想中专业化变量会产生另一个热带理想。这在理论中扮演了超平面部分的作用。我们还表明，消除理论（品种的投影）适用于在经典案例中的热带理想。定义热带理想的矩形条件对于这些结果至关重要。
Tropical ideals, introduced in arXiv:1609.03838, define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of the same dimension as the ideal. This means that every subscheme of a tropical toric variety defined by a tropical ideal has an associated class in the Chow ring of the toric variety. A key tool in the proof is that specialization of variables in a tropical ideal yields another tropical ideal; this plays the role of hyperplane sections in the theory. We also show that elimination theory (projection of varieties) works for tropical ideals as in the classical case. The matroid condition that defines tropical ideals is crucial for these results.
