{
  "id": "math/0702219",
  "version": "v3",
  "published": "2007-02-08T14:05:04.000Z",
  "updated": "2008-07-25T04:55:36.000Z",
  "title": "The genus zero Gromov-Witten invariants of [Sym^2 P^2]",
  "authors": [
    "Jonathan Wise"
  ],
  "comment": "33 pages; mostly rewritten, many errors corrected; all comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the Abramovich--Vistoli moduli space of genus zero orbifold stable maps to [Sym^2 P^2], the stack symmetric square of P^2. This compactifies the moduli space of stable maps from hyperelliptic curves to P^2, and we show that all genus zero Gromov--Witten invariants are determined from trivial enumerative geometry of hyperelliptic curves. We also show how the genus zero Gromov--Witten invariants can be used to determine the number of hyperelliptic curves of degree d and genus g interpolating 3d + 1 generic points in P^2. Comparing our method to that of Graber for calculating the same numbers, we verify an example of the crepant resolution conjecture.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-07-25T04:55:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "14N10"
    ],
    "keywords": [
      "genus zero gromov-witten invariants",
      "hyperelliptic curves",
      "genus zero orbifold stable maps",
      "crepant resolution conjecture",
      "abramovich-vistoli moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2219W"
    }
  }
}