{
  "id": "1310.8505",
  "version": "v3",
  "published": "2013-10-31T13:59:13.000Z",
  "updated": "2015-02-24T08:41:49.000Z",
  "title": "Minkowski decomposition and generators of the moving cone for toric varieties",
  "authors": [
    "Piotr Pokora",
    "David Schmitz",
    "Stefano Urbinati"
  ],
  "comment": "Version 2: one more section on how to perform a Minkowski decomposition for toric polytopes Version 3: minor changes",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that for smooth projective toric varieties, the Okounkov body of a $T$-invariant pseudo-effective divisor with respect to a $T$-invariant flag decomposes as a finite Minkowski sum of indecomposable polytopes. We prove that these indecomposable polytopes form a Minkowski base and that they correspond to the rays in the secondary fan. Moreover, we present an algorithm to find the Minkowski base.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-13T21:21:05.000Z",
      "comment": "Version 2: one more section on how to perform a Minkowski decomposition for toric polytopes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-24T08:41:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14M25"
    ],
    "keywords": [
      "minkowski decomposition",
      "moving cone",
      "minkowski base",
      "generators",
      "smooth projective toric varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8505P"
    }
  }
}