{
  "id": "1507.08397",
  "version": "v1",
  "published": "2015-07-30T06:48:45.000Z",
  "updated": "2015-07-30T06:48:45.000Z",
  "title": "Finite time collapsing of the Kähler-Ricci flow on threefolds",
  "authors": [
    "Valentino Tosatti",
    "Yuguang Zhang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first Chern class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-30T06:48:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C55",
      "14J45",
      "32Q15",
      "58J35",
      "14E30"
    ],
    "keywords": [
      "kähler-ricci flow",
      "compact kahler threefold",
      "finite time extinction",
      "finite time collapsing singularity",
      "first chern class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150708397T"
    }
  }
}