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Initial degenerations of Grassmannians
Selecta Mathematica ( IF 1.4 ) Pub Date : 2021-06-23 , DOI: 10.1007/s00029-021-00679-6
Daniel Corey

We construct closed immersions from initial degenerations of \({{\,\mathrm{Gr}\,}}_{0}(d,n)\)—the open cell in the Grassmannian \({{\,\mathrm{Gr}\,}}(d,n)\) given by the nonvanishing of all Plücker coordinates—to limits of thin Schubert cells associated to diagrams induced by the face poset of the corresponding tropical linear space. These are isomorphisms when (dn) equals (2, n), (3, 6) and (3, 7). As an application we prove \({{\,\mathrm{Gr}\,}}_0(3,7)\) is schön, and the Chow quotient of \({{\,\mathrm{Gr}\,}}(3,7)\) by the maximal torus in \( {\text {PGL}}(7)\) is the log canonical compactification of the moduli space of 7 points in \({\mathbb {P}}^2\) in linear general position, making progress on a conjecture of Hacking, Keel, and Tevelev.



中文翻译:

格拉斯曼人的初始退化

我们从\({{\,\mathrm{Gr}\,}}_{0}(d,n)\)的初始退化构建封闭浸入- Grassmannian \({{\,\mathrm{ Gr}\,}}(d,n)\)由所有 Plücker 坐标的非零给出 - 与由相应热带线性空间的面偏序诱导的图相关联的薄舒伯特单元的限制。当 ( d , n ) 等于 (2,  n )、(3, 6) 和 (3, 7)时, 这些是同构。作为一个应用,我们证明\({{\,\mathrm{Gr}\,}}_0(3,7)\)是 schön,并且\({{\,\mathrm{Gr}\,} }(3,7)\)\( {\text {PGL}}(7)\) 中的最大圆环是线性一般位置\({\mathbb {P}}^2\)中7 个点的模空间的对数规范紧缩,在 Hacking、Keel 和 Tevelev 的猜想上取得进展。

更新日期:2021-06-23
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