{
  "id": "math/9905034",
  "version": "v4",
  "published": "1999-05-05T21:15:07.000Z",
  "updated": "2000-02-09T18:30:36.000Z",
  "title": "Moduli Spaces of Higher Spin Curves and Integrable Hierarchies",
  "authors": [
    "Tyler J. Jarvis",
    "Takashi Kimura",
    "Arkady Vaintrob"
  ],
  "comment": "65 pages, postscript figures, AMS-LaTeX, uses Paul Taylor's diagrams.tex. Exposition improved. Many minor corrections made",
  "journal": "Compositio Mathematica 126:157-212 (2001)",
  "categories": [
    "math.AG",
    "math.DG",
    "math.QA"
  ],
  "abstract": "We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to Gelfand-Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a generating function which yields a solution of the semiclassical limit of the KdV_r equations. We formulate axioms for a cohomology class on this moduli space which allow one to construct a cohomological field theory of rank $r-1$ in all genera. In genus zero it produces a Frobenius manifold which is isomorphic to the Frobenius manifold structure on the base of the versal deformation of the A_{r-1} singularity. We prove analogs of the puncture, dilaton, and topological recursion relations by drawing an analogy with the construction of Gromov-Witten invariants and quantum cohomology.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2000-02-09T18:30:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "32G15",
      "81T40"
    ],
    "keywords": [
      "higher spin curves",
      "integrable hierarchies",
      "witten conjecture relating moduli spaces",
      "frobenius manifold structure",
      "genus zero part"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 499908,
      "adsabs": "1999math......5034J"
    }
  }
}