{
  "id": "math/0606180",
  "version": "v2",
  "published": "2006-06-08T09:43:16.000Z",
  "updated": "2006-10-12T01:38:13.000Z",
  "title": "Instanton counting and Donaldson invariants",
  "authors": [
    "Lothar Göttsche",
    "Hiraku Nakajima",
    "Kota Yoshioka"
  ],
  "comment": "45pages, typos corrected, update the reference to a new version of Mochizuki's paper math.AG/0210211",
  "categories": [
    "math.AG",
    "hep-th",
    "math.DG"
  ],
  "abstract": "For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture math.AG/0306198, hep-th/0306238, math.AG/0409441 and its refinement math.AG/0311058, we apply this result to give a generating function for the wallcrossing of Donaldson invariants of good walls of simply connected projective surfaces with $b_+=1$ in terms of modular forms. This formula was proved earlier in alg-geom/9506018 more generally for simply connected 4-manifolds with $b_+=1$, assuming the Kotschick-Morgan conjecture and it was also derived by physical arguments in hep-th/9709193.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-12T01:38:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D21",
      "57R57",
      "81T13",
      "81T60"
    ],
    "keywords": [
      "donaldson invariants",
      "instanton counting",
      "smooth projective toric surface",
      "nekrasov partition function",
      "nekrasov conjecture math"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 718921,
      "adsabs": "2006math......6180G"
    }
  }
}