{
  "id": "1910.13964",
  "version": "v1",
  "published": "2019-10-30T16:31:56.000Z",
  "updated": "2019-10-30T16:31:56.000Z",
  "title": "Stability of equivariant vector bundles over toric varieties",
  "authors": [
    "Jyoti Dasgupta",
    "Arijit Dey",
    "Bivas Khan"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We give a complete answer to the question of (semi)stability of tangent bundle of any nonsingular projective complex toric variety with Picard number 2 by using combinatorial crietrion of (semi)stability of an equivariant sheaf. We also give a complete answer to the question of (semi)stability of tangent bundle of all toric Fano 4-folds with Picard number (\\leq) 3 which are classified by Batyrev \\cite{batyrev}. We have constructed a collection of equivariant indecomposable rank 2 vector bundles on Bott tower and pseudo-symmetric toric Fano varieties. Further in case of Bott tower, we have shown the existence of an equivariant stable rank 2 vector bundle with certain Chern classes with respect to a suitable polarization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-30T16:31:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivariant vector bundles",
      "picard number",
      "bott tower",
      "pseudo-symmetric toric fano varieties",
      "tangent bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}