{
  "id": "math/0611945",
  "version": "v1",
  "published": "2006-11-30T12:20:31.000Z",
  "updated": "2006-11-30T12:20:31.000Z",
  "title": "K-theoretic Donaldson invariants via instanton counting",
  "authors": [
    "Lothar Göttsche",
    "Hiraku Nakajima",
    "Kota Yoshioka"
  ],
  "comment": "72 pages, 2 figures",
  "categories": [
    "math.AG",
    "hep-th",
    "math.DG"
  ],
  "abstract": "In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In particular, if X is a smooth projective toric surface, we determine these invariants and their wallcrossing in terms of the K-theoretic version of the Nekrasov partition function (called 5-dimensional supersymmetric Yang-Mills theory compactified on a circle in the physics literature). Using the results of math.AG/0606180 we give an explicit generating function for the wallcrossing of these invariants in terms of elliptic functions and modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-30T12:20:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14D21",
      "57R57",
      "81T13",
      "81T60"
    ],
    "keywords": [
      "k-theoretic donaldson invariants",
      "instanton counting",
      "supersymmetric yang-mills theory",
      "nekrasov partition function",
      "smooth projective toric surface"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4310/PAMQ.2009.v5.n3.a5"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 72,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 733244,
      "adsabs": "2006math.....11945G"
    }
  }
}