{
  "id": "2008.11419",
  "version": "v1",
  "published": "2020-08-26T07:20:31.000Z",
  "updated": "2020-08-26T07:20:31.000Z",
  "title": "Linearization of holomorphic families of algebraic automorphisms of the affine plane",
  "authors": [
    "Shigeru Kuroda",
    "Frank Kutzschebauch",
    "Tomasz Pełka"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-26T07:20:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "32M05",
      "14R10",
      "32M17",
      "32Q56"
    ],
    "keywords": [
      "affine plane",
      "holomorphic family",
      "smooth open riemann surface",
      "linearization",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}