{
  "id": "1303.1323",
  "version": "v4",
  "published": "2013-03-06T12:57:00.000Z",
  "updated": "2019-04-04T09:37:49.000Z",
  "title": "Tilting objects on tubular weighted projective lines: a cluster tilting approach",
  "authors": [
    "Jianmin Chen",
    "Yanan Lin",
    "Pin Liu",
    "Shiquan Ruan"
  ],
  "comment": "23 pages. Accepted for publication in SCIENCE CHINA Mathematics",
  "categories": [
    "math.RT"
  ],
  "abstract": "Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is constructed via cluster tilting mutation. Moreover, the cluster tilting approach also provides a new method to classify the endomorphism algebras of tilting objects in the category of coherent sheaves and the associated bounded derived category.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-11-10T15:05:24.000Z",
      "title": "Classification of tilting objects on a weighted projective line of type $(2,2,2,2;λ)$",
      "abstract": "Using cluster tilting theory, we investigate the tilting objects in the stable category of vector bundles on a weighted projective line of type $(2, 2, 2, 2; \\lambda)$. Furthermore, we classify the endomorphism algebras of tilting objects in the category of coherent sheaves and in its derived category.",
      "comment": "27 pages. arXiv admin note: text overlap with arXiv:1101.3675 by other authors without attribution",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2019-04-04T09:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "16G70",
      "16S99",
      "18E30"
    ],
    "keywords": [
      "weighted projective line",
      "tilting objects",
      "classification",
      "cluster tilting theory",
      "vector bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.1323C"
    }
  }
}