加法群的基本表示的分离簇
The separating variety for the basic representations of the additive group
摘要：
对于作用于仿射簇$X$的群$G$，分离簇是$X\times X$编码的闭子簇，其中$X$的点由不变量分离。本文主要研究特征为零的域的加法群的维数为$n+1$的不可分解有理线性表示$V_n$，并将分离簇分解为不可约分支的并.我们表明，如果$n$是奇数，整除4，或等于2，封闭的行动，它有维度$n+2$的图形，是唯一的组件的分离品种。在其余情况下，存在维度$n+1$的第二个不可约分量。我们的结论是，在这些情况下，没有多项式分离代数。
英文摘要：
For a group $G$ acting on an affine variety $X$, the separating variety is the closed subvariety of $X\times X$ encoding which points of $X$ are separated by invariants. We concentrate on the indecomposable rational linear representations $V_n$ of dimension $n+1$ of the additive group of a field of characteristic zero, and decompose the separating variety into the union of irreducible components. We show that if $n$ is odd, divisible by four, or equal to two, the closure of the graph of the action, which has dimension $n+2$, is the only component of the separating variety. In the remaining cases, there is a second irreducible component of dimension $n+1$. We conclude that in these cases, there are no polynomial separating algebras.
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