{
  "id": "1705.10048",
  "version": "v1",
  "published": "2017-05-29T06:38:09.000Z",
  "updated": "2017-05-29T06:38:09.000Z",
  "title": "Chow Rings of Mp_{0,2}(N,d) and Mbar_{0,2}(P^{N-1},d) and Gromov-Witten Invariants of Projective Hypersurfaces of Degree 1 and 2",
  "authors": [
    "Hayato Saito"
  ],
  "comment": "20 pages, 9 figures, AMSLaTeX",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we prove formulas that represent two-pointed Gromov-Witten invariant <O_{h^a}O_{h^b}>_{0,d} of projective hypersurfaces with d=1,2 in terms of Chow ring of Mbar_{0,2}(P^{N-1},d), the moduli spaces of stable maps from genus 0 stable curves to projective space P^{N-1}. Our formulas are based on representation of the intersection number w(O_{h^a}O_{h^b})_{0,d}, which was introduced by Jinzenji, in terms of Chow ring of Mp_{0,2}(N,d), the moduli space of quasi maps from P^1 to P^{N-1} with two marked points. In order to prove our formulas, we use the results on Chow ring of Mbar_{0,2}(P^{N-1},d), that were derived by A. Mustata and M. Mustata. We also present explicit toric data of Mp_{0,2}(N,d) and prove relations of Chow ring of Mp_{0,2}(N,d).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-29T06:38:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35"
    ],
    "keywords": [
      "chow ring",
      "projective hypersurfaces",
      "moduli space",
      "represent two-pointed gromov-witten invariant",
      "explicit toric data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}