{
  "id": "0704.2634",
  "version": "v4",
  "published": "2007-04-20T05:40:35.000Z",
  "updated": "2009-09-15T17:29:29.000Z",
  "title": "Instantons and curves on class VII surfaces",
  "authors": [
    "Andrei Teleman"
  ],
  "comment": "LaTeX 48 pages; RV: minor corrections, new paragraph dedicated to the structure of the moduli space around the circles of reductions; RV: minor corrections, to appear in Annals of Mathematics",
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV",
    "math.GT"
  ],
  "abstract": "We develop a general strategy, based on gauge theoretical methods, to prove existence of curves on class VII surfaces. We prove that, for $b_2=2$, every minimal class VII surface has a cycle of rational curves hence, by a result of Nakamura, is a global deformation of a one parameter family of blown up primary Hopf surfaces. The case $b_2=1$ has been solved in a previous article. The fundamental object intervening in our strategy is the moduli space ${\\mathcal M}^{\\pst}(0,{\\mathcal K})$ of polystable bundles ${\\mathcal E}$ with $c_2({\\mathcal E})=0$, $\\det({\\mathcal E})={\\mathcal K}$. For large $b_2$ the geometry of this moduli space becomes very complicated. The case $b_2=2$ treated here in detail requires new ideas and difficult techniques of both complex geometric and gauge theoretical nature.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-09-15T17:29:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "53C07",
      "32G13"
    ],
    "keywords": [
      "instantons",
      "moduli space",
      "minimal class vii surface",
      "primary hopf surfaces",
      "gauge theoretical methods"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 749019,
      "adsabs": "2007arXiv0704.2634T"
    }
  }
}