{
  "id": "1710.04351",
  "version": "v1",
  "published": "2017-10-12T03:22:20.000Z",
  "updated": "2017-10-12T03:22:20.000Z",
  "title": "Extended Okounkov bodies and multi-point Seshadri constants",
  "authors": [
    "Jaesun Shin"
  ],
  "comment": "33 pages, comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Based on the work of Okounkov, Lazarsfeld-Mustata and Kaveh-Khovanskii independently associated a convex body, called the Okounkov body, to a big divisor on a smooth projective variety with respect to an admissible flag. Although the Okounkov bodies carry rich positivity data of big divisors, they only provide information near a single point. The purpose of this paper is to introduce a convex body of a big divisor that is effective in handling the positivity theory associated with multi-point settings. These convex bodies open the door to approach the local positivity theory at multiple points from a convex-geometric perspective. We study their various properties and their shapes, and observe local positivity data via them. Finally, we give some applications, especially for the Nagata conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-12T03:22:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14J99"
    ],
    "keywords": [
      "multi-point seshadri constants",
      "okounkov body",
      "extended okounkov bodies",
      "convex body",
      "big divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}