{
  "id": "1711.07816",
  "version": "v1",
  "published": "2017-11-19T16:58:49.000Z",
  "updated": "2017-11-19T16:58:49.000Z",
  "title": "Admissible Pairs vs Gieseker--Maruyama",
  "authors": [
    "Nadezda V. Timofeeva"
  ],
  "comment": "20 pages. arXiv admin note: text overlap with arXiv:1411.7872",
  "categories": [
    "math.AG"
  ],
  "abstract": "A morphism of the moduli functor of admissible semistable pairs to the Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these functors are isomorphic, and the moduli scheme for semistable admissible pairs $((\\tilde S, \\tilde L), \\tilde E)$ is isomorphic to the Gieseker -- Maruyama moduli scheme. The considerations involve all components of moduli functors and corresponding moduli scheme as they exist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-19T16:58:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14D20"
    ],
    "keywords": [
      "admissible pairs",
      "gieseker-maruyama",
      "maruyama moduli scheme",
      "maruyama moduli functor",
      "semistable coherent torsion-free sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}