{
  "id": "1806.10380",
  "version": "v1",
  "published": "2018-06-27T09:55:38.000Z",
  "updated": "2018-06-27T09:55:38.000Z",
  "title": "Characterization of Ulrich bundles on Hirzebruch surfaces",
  "authors": [
    "Vincenzo Antonelli"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this work we characterize Ulrich bundles of any rank on polarized rational ruled surfaces over $\\mathbb{P}^1$. We show that every Ulrich bundle admits a resolution in terms of line bundles. Conversely, given an injective map between suitable totally decomposed vector bundles, we show that its cokernel is Ulrich if it satisfies a vanishing in cohomology. Finally we construct examples of indecomposable Ulrich bundles for several different polarizations and ranks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-27T09:55:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14F05",
      "14J26"
    ],
    "keywords": [
      "hirzebruch surfaces",
      "characterization",
      "ulrich bundle admits",
      "line bundles",
      "suitable totally decomposed vector bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}