论文标题
$ \ mathbb {c}^{8} $schön的3 planes的grassmannian
The Grassmannian of 3-planes in $\mathbb{C}^{8}$ is schön
论文作者
论文摘要
我们证明，Grassmannian $ \ operatatorName {gr}（3,8）$的开放子各种$ \ operatorname {gr} _0（3,8）$是由所有plücker坐标的不变确定的，即Schön，即其最初的初始变色。此外，我们发现了一个具有两个连接组件的初始变性，并表明其余的初始变性（直至对称性）是不可还原的。作为一个应用程序，我们证明了$ \ pereTatorName {gr}（3,8）$的盘子商的对角线$ \ operatatorName {pgl}（8）$是$ 8 $ $ \ \ nathbb {p} p}^2 $，concluce conclur forclun concluce concluce of concluce of tecl of concecl of tecl concecl of concluce concecl of concecl of foref的对数规范的压实。在此过程中，我们开发了各种技术来研究方案的有限逆极限。
We prove that the open subvariety $\operatorname{Gr}_0(3,8)$ of the Grassmannian $\operatorname{Gr}(3,8)$ determined by the nonvanishing of all Plücker coordinates is schön, i.e., all of its initial degenerations are smooth. Furthermore, we find an initial degeneration that has two connected components, and show that the remaining initial degenerations, up to symmetry, are irreducible. As an application, we prove that the Chow quotient of $\operatorname{Gr}(3,8)$ by the diagonal torus of $\operatorname{PGL}(8)$ is the log canonical compactification of the moduli space of $8$ lines in $\mathbb{P}^2$, resolving a conjecture of Hacking, Keel, and Tevelev. Along the way we develop various techniques to study finite inverse limits of schemes.
