LINEARIZATION OF HOLOMORPHIC FAMILIES OF ALGEBRAIC AUTOMORPHISMS OF THE AFFINE PLANE

KURODA, SHIGERU; KUTZSCHEBAUCH, Frank; PEŁKA, TOMASZ (2022). LINEARIZATION OF HOLOMORPHIC FAMILIES OF ALGEBRAIC AUTOMORPHISMS OF THE AFFINE PLANE. Transformation groups, 28(4), pp. 1607-1628. Springer 10.1007/s00031-021-09692-7

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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.

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