Given a homogeneous ideal I in a polynomial ring over a field, one may record, for each degree d and for each polynomial \(f\in I_d\), the set of monomials in f with nonzero coefficients. These data collectively form the tropicalization of I. Tropicalizing ideals induces a “matroid stratification” on any (multigraded) Hilbert scheme. Very little is known about the structure of these stratifications. In this paper, we explore many examples of matroid strata, including some with interesting combinatorial structure, and give a convenient way of visualizing them. We show that the matroid stratification in the Hilbert scheme of points \((\mathbb {P}^1)^{[k]}\) is generated by all Schur polynomials in k variables. We end with an application to the T-graph problem of \((\mathbb {A}^2)^{[n]};\) classifying this graph is a longstanding open problem, and we establish the existence of an infinite class of edges.

给定一个域上的多项式环中的齐次理想I，可以为每个度d和每个多项式\（f \ in_d \）记录f中具有非零系数的单项式集合。这些数据共同构成了I的热带化。理想化的热带化在任何（多层次的）希尔伯特方案上都引发了“拟阵分层”。这些分层的结构知之甚少。在本文中，我们探索了拟人岩层的许多示例，包括一些具有有趣组合结构的示例，并提供了可视化它们的便捷方法。我们证明了点\（（\ mathbb {P} ^ 1）^ {[k]} \）的Hilbert方案中的拟阵分层由k个变量中的所有Schur多项式生成。我们结束与一个应用程序到Ť的问题-图\（（\ mathbb {A} ^ 2）^ {[N]}; \）该曲线图是分类的长期未解决的问题，我们建立无限类的存在的边缘。