{
  "id": "1702.06252",
  "version": "v1",
  "published": "2017-02-21T03:22:42.000Z",
  "updated": "2017-02-21T03:22:42.000Z",
  "title": "Bridgeland stability conditions on surfaces with curves of negative self-intersection",
  "authors": [
    "Rebecca Tramel"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth complex projective variety. In 2002, Bridgeland defined a notion of stability for the objects in $D^b(X)$, the bounded derived category of coherent sheaves on $X$, which generalized the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on $X$ and the geometry of the variety. We construct new stability conditions for surfaces containing a curve $C$ whose self-intersection is negative. We show that these stability conditions lie on a wall of the geometric chamber of ${\\rm Stab}(X)$, the stability manifold of $X$. We then construct the moduli space $M_{\\sigma}(\\mathcal{O}_X)$ of $\\sigma$-semistable objects of class $[\\mathcal{O}_X]$ in $K_0(X)$ after wall-crossing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-21T03:22:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05"
    ],
    "keywords": [
      "bridgeland stability conditions",
      "negative self-intersection",
      "smooth complex projective variety",
      "stability conditions lie",
      "coherent sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}