{
  "id": "math/0411037",
  "version": "v3",
  "published": "2004-11-02T00:37:49.000Z",
  "updated": "2006-11-26T00:01:46.000Z",
  "title": "The local Gromov-Witten theory of curves",
  "authors": [
    "Jim Bryan",
    "Rahul Pandharipande"
  ],
  "comment": "Introduction rewritten, version to appear in JAMS",
  "categories": [
    "math.AG",
    "hep-th"
  ],
  "abstract": "The local Gromov-Witten theory of curves is solved by localization and degeneration methods. Localization is used for the exact evaluation of basic integrals in the local Gromov-Witten theory of P^1. A TQFT formalism is defined via degeneration to capture higher genus curves. Together, the results provide a compete and effective solution. The local Gromov-Witten theory of curves is equivalent to the local Donaldson-Thomas theory of curves, the quantum cohomology of the Hilbert scheme points of C^2, and the orbifold quantum cohomology the symmetric product of C^2. The results of the paper provide the local Gromov-Witten calculations required for the proofs of these equivalences.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-11-26T00:01:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35"
    ],
    "keywords": [
      "local gromov-witten theory",
      "capture higher genus curves",
      "local gromov-witten calculations",
      "local donaldson-thomas theory",
      "hilbert scheme points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 663547,
      "adsabs": "2004math.....11037B"
    }
  }
}