{
  "id": "1103.4352",
  "version": "v1",
  "published": "2011-03-22T19:15:30.000Z",
  "updated": "2011-03-22T19:15:30.000Z",
  "title": "Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces",
  "authors": [
    "Jason Lo",
    "Zhenbo Qin"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For the derived category of bounded complexes of sheaves on a smooth projective surface, Bridgeland and Arcara-Bertram constructed Bridgeland stability conditions $(Z_m, \\mathcal P_m)$ parametrized by $m \\in (0, +\\infty)$. In this paper, we show that the set of mini-walls in $(0, +\\infty)$ of a fixed numerical type is locally finite. In addition, we strengthen a result of Bayer by proving that the moduli of polynomial Bridgeland semistable objects of a fixed numerical type coincides with the moduli of $(Z_m, \\mathcal P_m)$-semistable objects whenever $m$ is larger than a universal constant depending only on the numerical type. We further identify the moduli of polynomial Bridgeland semistable objects with the Gieseker/Simpson moduli spaces and the Uhlenbeck compactification spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-22T19:15:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J10",
      "14D20"
    ],
    "keywords": [
      "derived category",
      "polynomial bridgeland semistable objects",
      "mini-walls",
      "arcara-bertram constructed bridgeland stability conditions",
      "fixed numerical type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.4352L"
    }
  }
}