{
  "id": "1604.02022",
  "version": "v1",
  "published": "2016-04-07T14:49:49.000Z",
  "updated": "2016-04-07T14:49:49.000Z",
  "title": "Positivity of anti-canonical divisors and $F$-purity of fibers",
  "authors": [
    "Sho Ejiri"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we prove that given a flat generically smooth morphism between smooth projective varieties with $F$-pure closed fibers, if the source space is Fano, weak Fano or a variety with the nef anti-canonical divisor, then so is the target space. We also show that relative anti-canonical divisors of generically smooth surjective nonconstant morphisms are not nef and big in arbitrary characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-07T14:49:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D06",
      "14J45"
    ],
    "keywords": [
      "positivity",
      "generically smooth surjective nonconstant morphisms",
      "flat generically smooth morphism",
      "arbitrary characteristic",
      "nef anti-canonical divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160402022E"
    }
  }
}