论文标题
对光滑的投射尺寸的交换行动
Commutative actions on smooth projective quadrics
论文作者
论文摘要
通过对$ p^{n+1} $的平滑四边形$ q_n $的换算行动，我们的意思是在$ q_n $上使用开放的轨道上的$ q_n $的有效行动。我们表明，对于$ n \ geq 3 $，$ q_n $上的所有交换措施都是Sharoiko在2009年描述的加性动作。因此，在$ q_n $上达到了唯一的交换措施。对于$ n = 2 $，在$ q_2 $上达到$ q_2 $的交换措施，$ n = 1 $，在$ q_1 $上有两种交换措施，直至等价。
By a commutative action on a smooth quadric $Q_n$ in $P^{n+1}$ we mean an effective action of a commutative connected algebraic group on $Q_n$ with an open orbit. We show that for $n \geq 3$ all commutative actions on $Q_n$ are additive actions described by Sharoiko in 2009. So there is a unique commutative action on $Q_n$ up to equivalence. For $n = 2$ there are three commutative actions on $Q_2$ up to equivalence, for $n = 1$ there are two commutative actions on $Q_1$ up to equivalence.
