{
  "id": "1110.0722",
  "version": "v3",
  "published": "2011-10-04T15:22:33.000Z",
  "updated": "2012-06-18T08:53:00.000Z",
  "title": "On the influence of the Segre Problem on the Mori cone of blown-up surfaces",
  "authors": [
    "Fulvio Di Sciullo"
  ],
  "comment": "19 pages, 2 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "We propose a generalization of SHGH Conjectures to a smooth projective surface Y: the so called Segre Problem. The study of linear systems on Y can be translated in terms of the Mori cone of the blow up $X = Bl_r Y$ at $r$ general points. Generalizing a result by de Fernex, we prove that if Segre Problem holds true, then a part of the Mori cone of $X$ does coincide with a part of the positive cone of $X$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-06-18T08:53:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30"
    ],
    "keywords": [
      "mori cone",
      "blown-up surfaces",
      "segre problem holds true",
      "smooth projective surface",
      "shgh conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.0722D"
    }
  }
}