{
  "id": "0710.5751",
  "version": "v1",
  "published": "2007-10-30T20:29:44.000Z",
  "updated": "2007-10-30T20:29:44.000Z",
  "title": "A Vanishing Result for Toric Varieties Associated with Root Systems",
  "authors": [
    "Qëndrim R. Gashi"
  ],
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Consider a root system $R$ and the corresponding toric variety $V_R$ whose fan is the Weyl fan and whose lattice of characters is given by the root lattice for $R$. We prove the vanishing of the higher cohomology groups for certain line bundles on $V_R$ by proving a purely combinatorial result for root systems. These results are related to a converse to Mazur's Inequality for (simply-connected) split reductive groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-30T20:29:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "root system",
      "toric varieties",
      "vanishing result",
      "higher cohomology groups",
      "corresponding toric variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5751G"
    }
  }
}