AI 中文总结
研究斜对称矩阵束轨道闭包的周环类，以六维复向量空间\(V\)相关的\(G\)为研究对象，通过Jordan - Kronecker标准型分类\(\operatorname{PGL}(V)\)在\(G\)上的\(11\)个轨道，计算其在舒伯特基中的周环类。
AI 中文摘要
设\(V\)是六维复向量空间，\(G = \operatorname{Gr}(2,\Lambda^2V^\vee)\)参数化斜对称\(6\times6\)矩阵束。\(\operatorname{PGL}(V)\)在\(G\)上有\(11\)个轨道，由Jordan - Kronecker标准型分类。我们在\(\operatorname{CH}^*(G)\)的舒伯特基中计算每个轨道闭包的周环类。
英文摘要
Let $V$ be a six-dimensional complex vector space and let $G=\operatorname{Gr}(2,Λ^2V^\vee)$ parametrize pencils of skew-symmetric $6\times6$ matrices. The group $\operatorname{PGL}(V)$ has $11$ orbits on $G$, classified by the Jordan-Kronecker canonical form. We compute the Chow class of every orbit closure in the Schubert basis of $\operatorname{CH}^*(G)$.
