{
  "id": "math/0607464",
  "version": "v2",
  "published": "2006-07-19T14:28:34.000Z",
  "updated": "2006-07-26T15:33:07.000Z",
  "title": "A cohomological interpretation of Brion's formula",
  "authors": [
    "Thomas Huettemann"
  ],
  "comment": "15 pages; uses Paul Taylor's \"diagrams\" and \"QED\" macro packages; v2: \"noetherian\" hypothesis removed, minor typos corrected",
  "journal": "Homology, Homotopy and Applications 9 (2007), No. 2, pp. 321-336",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "A subset K of R^n gives rise to a formal Laurent series with monomials corresponding to lattice points in K. Under suitable hypotheses, this series represents a rational function R(K). Michel Brion has discovered a surprising formula relating the rational function R(P) of a lattice polytope P to the sum of rational functions corresponding to the supporting cones subtended at the vertices of P. The result is re-phrased and generalised in the language of cohomology of line bundles on complete toric varieties. Brion's formula is the special case of an ample line bundle on a projective toric variety. - The paper also contains some general remarks on the cohomology of torus-equivariant line bundles on complete toric varieties, valid over noetherian ground rings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-26T15:33:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B20",
      "05A19",
      "14M25"
    ],
    "keywords": [
      "brions formula",
      "cohomological interpretation",
      "rational function",
      "complete toric varieties",
      "toric variety"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7464H"
    }
  }
}