论文标题
单型排的符号轨道
Symplectic orbits of unimodular rows
论文作者
论文摘要
对于平稳的仿射代数$ r $，尺寸$ d \ geq 3 $在field $ k $上和可变可倒数的矩阵$χ$等级$ 2n $，$ sp（χ）$ sp（χ）$ 2N $的可转让矩阵$ 2N $的$ 2N $ $ $超过$ r $ co $ um的$ quy um_ $ quy的$ r $同样}长度$ 2N $超过$ r $。在本文中，我们证明$ sp（χ）$在$ um_ {2n}（r）$上进行过渡，如果$ k $是代数关闭的，$ d！ \ in K^{\ times} $和$ 2N \ geq d $。
For a smooth affine algebra $R$ of dimension $d \geq 3$ over a field $k$ and an invertible alternating matrix $χ$ of rank $2n$, the group $Sp(χ)$ of invertible matrices of rank $2n$ over $R$ which are symplectic with respect to $χ$ acts on the right on the set $Um_{2n}(R)$ of unimodular rows of length $2n$ over $R$. In this paper, we prove that $Sp(χ)$ acts transitively on $Um_{2n}(R)$ if $k$ is algebraically closed, $d! \in k^{\times}$ and $2n \geq d$.
