{
  "id": "1401.1854",
  "version": "v2",
  "published": "2014-01-08T23:04:02.000Z",
  "updated": "2016-06-20T00:53:20.000Z",
  "title": "Pull-back of quasi-log structures",
  "authors": [
    "Osamu Fujino"
  ],
  "comment": "13 pages, v2: revision following referee's comments. arXiv admin note: text overlap with arXiv:0907.1506, arXiv:1202.5365",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that the pull-back of a quasi-log scheme by a smooth quasi-projective morphism has a natural quasi-log structure. We treat an application to log Fano pairs. This paper also contains a proof of the simple connectedness of log Fano pairs with only log canonical singularities by Kento Fujita.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-08T23:04:02.000Z",
      "abstract": "One of the main purposes of this paper is to make the theory of quasi-log schemes more flexible and more useful. More precisely, we prove that the pull-back of a quasi-log scheme by a smooth quasi-projective morphism has a natural quasi-log structure after clarifying the definition of quasi-log schemes. We treat some applications to singular Fano varieties. This paper also contains a proof of the simple connectedness of log canonical Fano varieties.",
      "comment": "25 pages. arXiv admin note: text overlap with arXiv:0907.1506",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-06-20T00:53:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "14J45"
    ],
    "keywords": [
      "quasi-log scheme",
      "log canonical fano varieties",
      "singular fano varieties",
      "natural quasi-log structure",
      "smooth quasi-projective morphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.1854F"
    }
  }
}