{
  "id": "1401.6149",
  "version": "v2",
  "published": "2014-01-23T20:20:05.000Z",
  "updated": "2015-09-14T22:26:00.000Z",
  "title": "Bridgeland Stability of Line Bundles on Surfaces",
  "authors": [
    "Daniele Arcara",
    "Eric Miles"
  ],
  "comment": "32 pages, 11 figures, updated based on referee report, to appear in JPAA",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the Bridgeland stability of line bundles on surfaces using Bridgeland stability conditions determined by divisors. We show that given a smooth projective surface $S$, a line bundle $L$ is always Bridgeland stable for those stability conditions if there are no curves $C\\subseteq S$ of negative self-intersection. When a curve $C$ of negative self-intersection is present, $L$ is destabilized by $L(-C)$ for some stability conditions. We conjecture that line bundles of the form $L(-C)$ are the only objects that can destabilize $L$, and that torsion sheaves of the form $L(C)|_C$ are the only objects that can destabilize $L[1]$. We prove our conjecture in several cases, and in particular for Hirzebruch surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-23T20:20:05.000Z",
      "comment": "28 pages, 8 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-14T22:26:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "line bundle",
      "negative self-intersection",
      "smooth projective surface",
      "bridgeland stability conditions",
      "hirzebruch surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6149A"
    }
  }
}