{
  "id": "1903.04317",
  "version": "v1",
  "published": "2019-03-11T14:17:13.000Z",
  "updated": "2019-03-11T14:17:13.000Z",
  "title": "Volume of line bundles via valuation vectors (different from Okounkov bodies)",
  "authors": [
    "Oliver Braunling"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Up to a factor 1/n!, the volume of a big line bundle agrees with the Euclidean volume of its Okounkov body. The latter is the convex hull of top rank valuation vectors of sections, all with respect to a single flag. In this text we give a different volume formula, valid in the ample cone, also based on top rank valuation vectors, but mixing data along several different flags.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-11T14:17:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "13F30"
    ],
    "keywords": [
      "okounkov body",
      "rank valuation vectors",
      "big line bundle",
      "ample cone",
      "euclidean volume"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}