{
  "id": "1007.4270",
  "version": "v1",
  "published": "2010-07-24T13:56:35.000Z",
  "updated": "2010-07-24T13:56:35.000Z",
  "title": "Newton polytopes for horospherical spaces",
  "authors": [
    "Kiumars Kaveh",
    "A. G. Khovanskii"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "A subgroup H of a reductive group G is horospherical if it contains a maximal unipotent subgroup. We describe the Grothendieck semigroup of invariant subspaces of regular functions on G/H as a semigroup of convex polytopes. From this we obtain a formula for the number of solutions of a generic system of equations on G/H in terms of mixed volume of polytopes. This generalizes Bernstein-Kushnirenko theorem from toric geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-24T13:56:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M17",
      "14M25"
    ],
    "keywords": [
      "newton polytopes",
      "horospherical spaces",
      "maximal unipotent subgroup",
      "generalizes bernstein-kushnirenko theorem",
      "grothendieck semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4270K"
    }
  }
}