标题： 关于 $\text{Gr}(3,6)$中 PGL(3) 的余维 1 轨道闭包 显示英文标题

标题： On the codimension 1 PGL(3) orbit closures in $\text{Gr}(3,6)$

摘要： 射影线性群$\text{PGL}(3)$自然地作用在向量空间$V_2$中的三变量齐次二次曲线的$3$维子空间的Grassmannian$\text{Gr}(3, V_2)$上。Abdallah、Emsalem 和 Iarrobino 在2021年证明了这个作用有一个一参数轨道族以及14个特殊轨道。该作用的余维数1轨道由整个一参数轨道族以及14个特殊轨道中的2个组成。在本文中，我们计算了$\text{Gr}(3, V_2)$的Chow环中余维数1轨道闭包的类。 显示英文摘要

摘要： The projective linear group $\text{PGL}(3)$ naturally acts on the Grassmannian $\text{Gr}(3, V_2)$ of $3$-dimensional subspaces of the vector space $V_2$ of homogeneous conics in 3 variables. It was proved by Abdallah, Emsalem and Iarrobino in 2021 that this action has a one-parameter family of orbits along with 14 special orbits. The codimension 1 orbits of this action consist of the entire one-parameter family of orbits, along with 2 of the 14 special orbits. In this paper, we calculate the classes of the codimension 1 orbit closures in the Chow ring of $\text{Gr}(3, V_2)$.