{
  "id": "1209.6447",
  "version": "v2",
  "published": "2012-09-28T08:18:23.000Z",
  "updated": "2012-10-02T15:32:27.000Z",
  "title": "Automorphisms of surfaces of general type with q>=2 acting trivially in cohomology",
  "authors": [
    "Jin-Xing Cai",
    "Wenfei Liu",
    "Lei Zhang"
  ],
  "comment": "18 pages; a remark and a closely relevant reference are added",
  "categories": [
    "math.AG"
  ],
  "abstract": "A compact complex manifold X is said to be rationally cohomologically rigidified if its automorphism group Aut(X) acts faithfully on the cohomology ring H*(X,Q). In this note, we prove that, surfaces of general type with irregularity q>2 are rationally cohomologically rigidified, and so are minimal surfaces S with q=2 unless K^2=8X. This answers a question of Fabrizio Catanese in part. As examples we give a complete classification of surfaces isogenous to a product with q=2 that are not rationally cohomologically rigidified. These surfaces turn out however to be rigidified.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-02T15:32:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J50",
      "14J29"
    ],
    "keywords": [
      "general type",
      "cohomology",
      "automorphism group aut"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}