{
  "id": "1011.6306",
  "version": "v2",
  "published": "2010-11-29T17:47:53.000Z",
  "updated": "2011-05-04T17:43:39.000Z",
  "title": "Moduli of PT-semistable objects II",
  "authors": [
    "Jason Lo"
  ],
  "comment": "34 pages. Exposition improved based on referee's comments, especially the proofs of Prop 2.6 and 2.17 (of this version). References added; typos corrected. Openness and separatedness now in a separate section. Sections 4 and 5 of previous version removed. Accepted for publication by the Transactions of the American Mathematical Society. This is the sequel to http://arxiv.org/abs/1011.5688",
  "categories": [
    "math.AG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ as an Artin stack of finite type that is universally closed. In the absence of strictly semistable objects, we construct the moduli as a proper algebraic space of finite type.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-04T17:43:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14D20",
      "18E30",
      "14J60",
      "14J30"
    ],
    "keywords": [
      "pt-semistable objects",
      "finite type",
      "proper algebraic space",
      "smooth projective three-fold",
      "flat families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.6306L"
    }
  }
}