{
  "id": "math/0009109",
  "version": "v4",
  "published": "2000-09-11T18:03:12.000Z",
  "updated": "2001-04-21T16:10:14.000Z",
  "title": "Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces",
  "authors": [
    "Eyal Markman"
  ],
  "comment": "Latex, 23 pages. The introduction is expanded, the coefficient in part 3 of Theorem 1 is corrected, plus several other minor changes",
  "journal": "Journal fur die reine und angewandte Mathematik 544 (2002), 61-82",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let M be a moduli space of stable sheaves on a K3 or Abelian surface S. We express the class of the diagonal in the cartesian square of M in terms of the Chern classes of a universal sheaf. Consequently, we obtain generators of the cohomology ring of M. When S is a K3 and M is the Hilbert scheme of length n subschemes, this set of generators is sufficiently small in the sense that there aren't any relations among them in the stable cohomology ring. When S is the cotangent bundle of a Riemann surface, we recover the result of T. Hausel and M. Thaddeus: The cohomology ring of the moduli spaces of Higgs bundles is generated by the universal classes.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2001-04-21T16:10:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cohomology ring",
      "moduli space",
      "symplectic surfaces",
      "generators",
      "riemann surface"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9109M"
    }
  }
}