论文标题
仿射平面代数自动形态的全态家族的线性化
Linearization of holomorphic families of algebraic automorphisms of the affine plane
论文作者
论文摘要
令$ g $为一个还原组。我们证明，$ g $的多项式动作家族在$ \ mathbb {c}^2 $上，由开放的Riemann Surface进行了holomorphiles的参数，是可线化的。作为一个应用程序，我们表明$ \ mathbb {c}^3 $上的一类还原组动作是可线化的。我们证明的主要步骤是为$ \ mathbb {c}^2 $的Equivariant代数自动形态组建立一定的限制性OKA属性。
Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular class of reductive group actions on $\mathbb{C}^3$ is linearizable. The main step of our proof is to establish a certain restrictive Oka property for groups of equivariant algebraic automorphisms of $\mathbb{C}^2$.
