论文标题
标志品种的初始退化
Initial degenerations of flag varieties
论文作者
论文摘要
我们证明，标志品种的初始退化允许封闭的浸入有限的flag矩阵地层的逆极限，其中该图衍生自合适的标志矩阵多面体的矩阵细分。作为一个应用程序，我们证明了$ \ operatatorName {f \ ell}^{\ circ}（n）$的初始退化 - 完整的标志品种$ \ operatorname {f \ ell}（f \ ell}（n）$的开放子变量，包括一般位置 - 一般且不符合$ n $ n $ n \ leq leq 4 $。我们还通过$ \ operatatorName {pgl}（n）$的对角圆环研究$ \ operatatorName {f \ ell}（n）$的ChOW商，并证明，对于$ n = 4 $，这是其日志经典型号的日志毛茸茸的分辨率。
We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal subdivisions of a suitable flag matroid polytope. As an application, we prove that the initial degenerations of $\operatorname{F\ell}^{\circ}(n)$ -- the open subvariety of the complete flag variety $\operatorname{F\ell}(n)$ consisting of flags in general position -- are smooth and irreducible when $n\leq 4$. We also study the Chow quotient of $\operatorname{F\ell}(n)$ by the diagonal torus of $\operatorname{PGL}(n)$, and show that, for $n=4$, this is a log crepant resolution of its log canonical model.
