LINEARIZATION OF HOLOMORPHIC FAMILIES OF ALGEBRAIC AUTOMORPHISMS OF THE AFFINE PLANE

Let G be a reductive group. We prove that a family of polynomial actions of G on 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 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 ℂ^2.