{
  "id": "1811.02603",
  "version": "v1",
  "published": "2018-11-06T19:25:04.000Z",
  "updated": "2018-11-06T19:25:04.000Z",
  "title": "On exterior powers of the tangent bundle on toric varieties",
  "authors": [
    "David Schmitz"
  ],
  "comment": "11 pages, comments very welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the positivity of exterior powers of the tangent sheaf on toric varieties in order to generalize results by Campana and Peternell about 3-folds with nef second exterior power of the tangent bundle. Using the theory of equivariant vector bundles and the toric MMP, we establish in the smooth case a criterion for the positivity of $\\Lambda^m\\mathcal T_X$ in terms of wall relations. As an application, we classify smooth toric varieties of arbitrary dimension $n\\ge3$ with $\\Lambda^2\\mathcal T_X$ nef and those of dimension $n\\ge 4$ with $\\Lambda^3\\mathcal T_X$ ample.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T19:25:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14M25"
    ],
    "keywords": [
      "tangent bundle",
      "nef second exterior power",
      "equivariant vector bundles",
      "classify smooth toric varieties",
      "positivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}