{
  "id": "1710.00986",
  "version": "v1",
  "published": "2017-10-03T05:17:50.000Z",
  "updated": "2017-10-03T05:17:50.000Z",
  "title": "t-stabilities for a weighted projective line",
  "authors": [
    "Shiquan Ruan",
    "Xintian Wang"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "This present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev--Kuleshov--Rudakov. We give an equivalent description for the finest t-stability on a piecewise hereditary triangulated category. Moreover, for the bounded derived category $D^b(\\rm{coh}\\mathbb{X})$ of the category $\\rm{coh}\\mathbb{X}$ of coherent sheaves on the weighted projective line $\\mathbb{X}$ of weight type (2), we describe the semistable subcategories and final HN triangles for (exceptional) coherent sheaves. Furthermore, after introducing the notion of a t-exceptional sequence on a triangulated category, we show the existence of a t-exceptional triple for $D^b(\\rm{coh}\\mathbb{X})$. As an application, we obtain that each stability condition $\\sigma$ in the sense of Bridgeland admits a $\\sigma$-exceptional triple for the acyclic triangular quiver $Q$, which was first shown by Dimitrov--Katzarkov. We remark that this implies the connectedness of the space of stability conditions associated to $Q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-03T05:17:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E10",
      "18E30",
      "16G20",
      "14F05",
      "16G70"
    ],
    "keywords": [
      "weighted projective line",
      "stability condition",
      "coherent sheaves",
      "final hn triangles",
      "acyclic triangular quiver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}