{
  "id": "0902.2521",
  "version": "v2",
  "published": "2009-02-15T23:23:22.000Z",
  "updated": "2009-10-14T05:36:09.000Z",
  "title": "Okounkov bodies and restricted volumes along very general curves",
  "authors": [
    "Shin-Yao Jow"
  ],
  "comment": "15 pages; typos corrected and references updated; to appear in Advances in Mathematics",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a big divisor $D$ on a normal complex projective variety $X$, we show that the restricted volume of $D$ along a very general complete-intersection curve $C\\subset X$ can be read off from the Okounkov body of $D$ with respect to an admissible flag containing $C$. From this we deduce that if two big divisors $D_1$ and $D_2$ on $X$ have the same Okounkov body with respect to every admissible flag, then $D_1$ and $D_2$ are numerically equivalent.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-14T05:36:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20"
    ],
    "keywords": [
      "okounkov body",
      "restricted volume",
      "general curves",
      "big divisor",
      "general complete-intersection curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2521J"
    }
  }
}