Linearization of holomorphic families of algebraic automorphisms of the affine plane

Shigeru Kuroda, Frank Kutzschebauch, Tomasz Pełka

Published 2020-08-26Version 1

Let $G$ be a reductive group. We prove that a holomorphic family of polynomial actions of $G$ on the complex plane $\mathbb{C}^2$, holomorphically parametrized by a smooth open Riemann surface, is linearizable. In particular, a certain class of actions of reductive groups on $\mathbb{C}^3$ is linearizable. Our main tool is some restrictive Oka property for groups of equivariant algebraic automorphisms of the complex plane, which we prove in this article.