We construct a family of compactifications of the affine cone of the Grassmannian variety of $2$ -planes. We show that both the tropical variety of the Plücker ideal and familiar valuations associated to the construction of Newton–Okounkov bodies for the Grassmannian variety can be recovered from these compactifications. In this way, we unite various perspectives for constructing toric degenerations of flag varieties.

中文翻译：

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来自紧实化的平面的 Grassmannian 的热带几何和 Newton-Okounkov 锥

我们构建了一系列 $2$ -planes 的Grassmannian 仿射锥的紧化族。我们表明，Plücker 理想的热带变体和与格拉斯曼变体的牛顿-奥昆科夫体构造相关的熟悉估值都可以从这些紧化中恢复。通过这种方式，我们将各种观点结合起来构建标志品种的复曲面退化。