{
  "id": "math/0603736",
  "version": "v2",
  "published": "2006-03-31T09:42:11.000Z",
  "updated": "2007-08-06T10:08:19.000Z",
  "title": "On Q-conic bundles",
  "authors": [
    "Shigefumi Mori",
    "Yuri Prokhorov"
  ],
  "comment": "54 pages, LaTeX",
  "journal": "Publ. Res. Inst. Math. Sci., 2008, 44, 315-369",
  "categories": [
    "math.AG"
  ],
  "abstract": "A $\\mathbb Q$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of $\\mathbb Q$-conic bundles near their singular fibers. One corollary to our main results is that the base surface of every $\\mathbb Q$-conic bundle has only Du Val singularities of type A (a positive solution of a conjecture by Iskovskikh). We obtain the complete classification of $\\mathbb Q$-conic bundles under the additional assumption that the singular fiber is irreducible and the base surface is singular.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-06T10:08:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30",
      "14E35",
      "14E30"
    ],
    "keywords": [
      "q-conic bundles",
      "singular fiber",
      "base surface",
      "additional assumption",
      "normal surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3736M"
    }
  }
}