{
  "id": "0806.2527",
  "version": "v1",
  "published": "2008-06-16T09:15:53.000Z",
  "updated": "2008-06-16T09:15:53.000Z",
  "title": "Torelli theorem for the moduli spaces of pairs",
  "authors": [
    "Vicente Munoz"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a smooth projective curve of genus at least two over the complex numbers. A pair (E,\\phi) over X consists of an algebraic vector bundle E over X and a holomorphic section \\phi of E. There is a concept of stability for pairs which depends on a real parameter \\tau. Here we prove that the third cohomology groups of the moduli spaces of \\tau-stable pairs with fixed determinant and rank at least two are polarised pure Hodge structures, and they are isomorphic to H^1(X) with its natural polarisation (except in very few exceptional cases). This implies a Torelli theorem for such moduli spaces. We recover that the third cohomology group of the moduli space of stable bundles of rank at least two and fixed determinant is a polarised pure Hodge structure, which is isomorphic to H^1(X). We also prove Torelli theorems for the corresponding moduli spaces of pairs and bundles with non-fixed determinant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-16T09:15:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F45",
      "14D20",
      "14H60"
    ],
    "keywords": [
      "moduli space",
      "torelli theorem",
      "polarised pure hodge structure",
      "third cohomology group",
      "fixed determinant"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1017/S0305004108002156",
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 2008,
      "month": "Dec",
      "volume": 146,
      "number": 3,
      "pages": 675
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008MPCPS.146..675M"
    }
  }
}