{
  "id": "math/9903124",
  "version": "v1",
  "published": "1999-03-22T11:41:34.000Z",
  "updated": "1999-03-22T11:41:34.000Z",
  "title": "Generalized periods and mirror symmetry in dimensions n>3",
  "authors": [
    "Sergey Barannikov"
  ],
  "comment": "51 pages, LaTeX",
  "categories": [
    "math.AG",
    "math.AC",
    "math.QA"
  ],
  "abstract": "The predictions of the Mirror Symmetry are extended in dimensions n>3 and are proven for projective complete intersections Calabi-Yau varieties. Precisely, we prove that the total collection of rational Gromov-Witten invariants of such variety can be expressed in terms of certain invariants of a new generalization of variation of Hodge structures attached to the dual variety. To formulate the general principles of Mirror Symmetry in arbitrary dimension it is necessary to introduce the ``extended moduli space of complex structures'' M. An analog M\\to H*(X,C)[n] of the classical period map is described and is shown to be a local isomorphism. The invariants of the generalized variations of Hodge structures are introduced. It is proven that their generating function satisfies the system of WDVV-equations exactly as in the case of Gromov-Witten invariants. The basic technical tool utilized is the Deformation theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-03-22T11:41:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q30"
    ],
    "keywords": [
      "mirror symmetry",
      "generalized periods",
      "hodge structures",
      "projective complete intersections calabi-yau varieties",
      "rational gromov-witten invariants"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......3124B"
    }
  }
}