{
  "id": "1210.7692",
  "version": "v2",
  "published": "2012-10-29T15:38:22.000Z",
  "updated": "2022-07-20T06:25:28.000Z",
  "title": "Arithmetic positivity on toric varieties",
  "authors": [
    "Jose Ignacio Burgos Gil",
    "Atsushi Moriwaki",
    "Patrice Philippon",
    "Martin Sombra"
  ],
  "comment": "54 pages, published in Journal of Algebraic Geometry 25 (2016) 201-272. The present version corrects a mistake in the published version of Corollary 6.2",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We continue with our study of the arithmetic geometry of toric varieties. In this text, we study the positivity properties of metrized R-divisors in the toric setting. For a toric metrized R-divisor, we give formulae for its arithmetic volume and its chi-arithmetic volume, and we characterize when it is arithmetically ample, nef, big or pseudo-effective, in terms of combinatorial data. As an application, we prove a Dirichlet's unit theorem on toric varieties, we give a characterization for the existence of a Zariski decomposition of a toric metrized R-divisor, and we prove a toric arithmetic Fujita approximation theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-29T15:38:22.000Z",
      "comment": "53 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2022-07-20T06:25:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "14G40",
      "52A41"
    ],
    "keywords": [
      "toric varieties",
      "arithmetic positivity",
      "toric arithmetic fujita approximation theorem",
      "toric metrized r-divisor",
      "dirichlets unit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7692B"
    }
  }
}