{
  "id": "1207.2085",
  "version": "v2",
  "published": "2012-07-09T15:53:05.000Z",
  "updated": "2013-05-24T23:47:23.000Z",
  "title": "Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations",
  "authors": [
    "Dan Abramovich",
    "Steffen Marcus",
    "Jonathan Wise"
  ],
  "comment": "42 pages. Some minor changes. To appear in Annales de l'Institut Fourier",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider four approaches to relative Gromov-Witten theory and Gromov-Witten theory of degenerations: Jun Li's original approach, Bumsig Kim's logarithmic expansions, Abramovich-Fantechi's orbifold expansions, and a logarithmic theory without expansions due to Gross-Siebert and Abramovich-Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov-Witten invariants associated to all four of these theories are identical.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-24T23:47:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "14H10",
      "14D23",
      "14D06",
      "14A20"
    ],
    "keywords": [
      "gromov-witten invariants",
      "comparison theorems",
      "smooth pairs",
      "degenerations",
      "bumsig kims logarithmic expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2085A"
    }
  }
}