{
  "id": "0807.2477",
  "version": "v2",
  "published": "2008-07-15T22:44:42.000Z",
  "updated": "2008-12-28T14:39:01.000Z",
  "title": "Noether-Lefschetz theory and the Yau-Zaslow conjecture",
  "authors": [
    "A. Klemm",
    "D. Maulik",
    "R. Pandharipande",
    "E. Scheidegger"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AG",
    "hep-th",
    "math.SG"
  ],
  "abstract": "The Yau-Zaslow conjecture determines the reduced genus 0 Gromov-Witten invariants of K3 surfaces in terms of the Dedekind eta function. Classical intersections of curves in the moduli of K3 surfaces with Noether-Lefschetz divisors are related to 3-fold Gromov-Witten theory via the K3 invariants. Results by Borcherds and Kudla-Millson determine the classical intersections in terms of vector-valued modular forms. Proven mirror transformations can often be used to calculate the 3-fold invariants which arise. Via a detailed study of the STU model (determining special curves in the moduli of K3 surfaces), we prove the Yau-Zaslow conjecture for all curve classes on K3 surfaces. Two modular form identities are required. The first, the Klemm-Lerche-Mayr identity relating hypergeometric series to modular forms after mirror transformation, is proven here. The second, the Harvey-Moore identity, is proven by D. Zagier and presented in the paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-28T14:39:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noether-lefschetz theory",
      "k3 surfaces",
      "klemm-lerche-mayr identity relating hypergeometric series",
      "proven mirror transformations",
      "dedekind eta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2477K"
    }
  }
}