{
  "id": "2202.12523",
  "version": "v1",
  "published": "2022-02-25T06:54:18.000Z",
  "updated": "2022-02-25T06:54:18.000Z",
  "title": "Special triple covers of algebraic surfaces",
  "authors": [
    "Nicolina Istrati",
    "Piotr Pokora",
    "Sönke Rollenske"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study special triple covers $f\\colon T \\to S$ of algebraic surfaces, where the Tschirnhausen bundle $\\mathcal E = \\left(f_*\\mathcal O_T/\\mathcal O_S\\right)^\\vee$ is a quotient of a split rank three vector bundle, and we provide several necessary and sufficient criteria for the existence. As an application, we give a complete classification of special triple planes, finding among others two nice families of K3 surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-25T06:54:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J10",
      "14J29"
    ],
    "keywords": [
      "algebraic surfaces",
      "study special triple covers",
      "special triple planes",
      "nice families",
      "tschirnhausen bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}