{
  "id": "2108.04868",
  "version": "v1",
  "published": "2021-08-10T18:39:54.000Z",
  "updated": "2021-08-10T18:39:54.000Z",
  "title": "Unchaining surgery, branched covers, and pencils on elliptic surfaces",
  "authors": [
    "Terry Fuller"
  ],
  "comment": "24 pages, 32 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We show that every member of an infinite family of symplectic manifolds constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden (arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1) the symplectic Calabi-Yau 4-manifolds among their family are diffeomorphic to the standard K3 surface; (2) each elliptic surface E(n) admits a genus g Lefschetz pencil, for all g greater than or equal to n; and (3) each elliptic surface E(n) blown up once admits a pair of inequivalent genus g Lefschetz pencils, for all g greater than or equal to n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-10T18:39:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic surface",
      "branched covers",
      "unchaining surgery",
      "lefschetz pencil",
      "standard k3 surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}