{
  "id": "1312.5549",
  "version": "v2",
  "published": "2013-12-19T13:49:22.000Z",
  "updated": "2016-02-05T15:50:18.000Z",
  "title": "Very general monomial valuations of $\\mathbb{P}^2$ and a Nagata type conjecture",
  "authors": [
    "Marcin Dumnicki",
    "Brian Harbourne",
    "Alex Küronya",
    "Joaquim Roé",
    "Tomasz Szemberg"
  ],
  "comment": "25 pages, 2 figures. Updated version of the Oberwolfach Preprint OWP 2013-22, with some new material. Comments welcome",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "It is well known that multi-point Seshadri constants for a small number $s$ of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their values are maximal for $s\\geq 9$ points. Tackling the problem in the language of valuations one can make sense of $s$ points for any positive real $s\\geq 1$. We show somewhat surprisingly that a Nagata-type conjecture should be valid for $s\\geq 8+1/36$ points and we compute explicitly all Seshadri constants (expressed here as the asymptotic maximal vanishing element) for $s\\leq 7+1/9$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-19T13:49:22.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-05T15:50:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nagata type conjecture",
      "general monomial valuations",
      "multi-point seshadri constants",
      "asymptotic maximal vanishing element",
      "small number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5549D"
    }
  }
}