{
  "id": "1802.08699",
  "version": "v1",
  "published": "2018-02-23T19:02:57.000Z",
  "updated": "2018-02-23T19:02:57.000Z",
  "title": "Local effectivity in projective spaces",
  "authors": [
    "Marcin Dumnicki",
    "Tomasz Szemberg",
    "Justyna Szpond"
  ],
  "comment": "17 pages, initial submission, comments welcome",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "In this note we introduce a Waldschmidt decomposition of divisors which might be viewed as a generalization of Zariski decomposition based on the effectivity rather than the nefness of divisors. As an immediate application we prove a recursive formula providing new effective lower bounds on Waldschmidt constants of very general points in projective spaces. We use these bounds in order to verify Demailly's conjecture in a number of new cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-23T19:02:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14J26",
      "14N20",
      "13A15",
      "13F20"
    ],
    "keywords": [
      "projective spaces",
      "local effectivity",
      "waldschmidt decomposition",
      "immediate application",
      "effective lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}