{
  "id": "1710.01484",
  "version": "v1",
  "published": "2017-10-04T07:11:42.000Z",
  "updated": "2017-10-04T07:11:42.000Z",
  "title": "Properness criteria for families of coherent analytic sheaves",
  "authors": [
    "Matei Toma"
  ],
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We extend Langton's valuative criterion for families of coherent algebraic sheaves to a complex analytic set-up. As a consequence we derive a set of sufficient conditions for the compactness of a moduli space of semistable sheaves over a compact complex manifold. This applies also to some cases appearing in complex projective geometry not covered by previous results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-04T07:11:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G13",
      "14D20"
    ],
    "keywords": [
      "coherent analytic sheaves",
      "properness criteria",
      "complex analytic set-up",
      "extend langtons valuative criterion",
      "coherent algebraic sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}