Reductive group actions with one-dimensional quotient
Reductive group actions with one-dimensional quotient
复制标题
具有一维商的还原群作用
DOI：
10.1007/bf02699430
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Gerald W. Schwarz
中科院分区：
文献类型：
--
作者：
H. Kraft;Gerald W. Schwarz
设G是代数作用在复仿射/i-空间A”= X上的约化复代数群。线性化问题询问是否每个这样的作用都代数等价于线性作用，即是否存在G-等变同构（p：X^> V，其中V是G-模。另一种表述这个问题的方法是：仿射克雷莫纳群Aut（A”）的每个约化子群是否共轭到GL^的子群？关于这个问题的详细报告可以在[Kri]中找到，在那里我们还描述了与其他经典问题的联系，例如
Let G be a reductive complex algebraic group acting algebraically on complex affine/i-space A"=: X. The Linearization Problem asks whether every such action is algebraically equivalent to a linear action, ie, whether there is a G-equivariant isomorphism (p: X^> V where V is a G-module. Another way to state this problem is the following: Is every reductive subgroup of the affine Cremona group Aut (A") conjugate to a subgroup of GL^? A detailed report on this question can be found in [Kri], where we also describe connections with other classical problems such as the