{
  "id": "math/0701521",
  "version": "v1",
  "published": "2007-01-18T20:00:18.000Z",
  "updated": "2007-01-18T20:00:18.000Z",
  "title": "On rationality of nonsingular threefolds with a pencil of Del Pezzo surfaces of degree 4",
  "authors": [
    "Constantin Shramov"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove a criterion of nonsingularity of a complete intersection of two fiberwise quadrics in a scroll over $P^1$. As a corollary we derive the following addition to the Alexeev theorem on rationality of standard Del Pezzo fibrations of degree 4 over $P^1$: we prove that any fibration of this kind with the topological Euler characteristic -4 is rational.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-18T20:00:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E08",
      "14E05"
    ],
    "keywords": [
      "del pezzo surfaces",
      "nonsingular threefolds",
      "rationality",
      "standard del pezzo fibrations",
      "alexeev theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1521S"
    }
  }
}