{
  "annotation_id": "876d401e-3d8f-4abb-b151-5da6c9b604e5",
  "date_created": "2026-03-02T18:02:51.293000Z",
  "date_modified": "2026-03-02T18:02:51.293000Z",
  "file_hash": "7d5979dd05ed8defa36f615f25d575e58aa7f4ceed496b43d2485322199a9230",
  "private": false,
  "record": {
    "abstract": "The Schwarzian equations satisfied by certain Hauptmoduls (i.e., uniformizing\nfunctions for Riemann surfaces of genus zero) are derived from the Picard-Fuchs\nequations for families of elliptic curves and associated surfaces. The\ninhomogeneous Picard-Fuchs equations associated to elliptic integrals with\nvarying endpoints are derived and used to determine solutions of equations that\nare algebraically related to a class of Painlev\\\u0027e VI equations.",
    "arxiv_id": "solv-int/9902013",
    "authors": [
      "J. Harnad"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "math-ph",
      "math.AG",
      "math.GR",
      "math.MP",
      "math.NT",
      "nlin.SI"
    ],
    "journal_ref": "Integrability: The Seiberg-Witten and Witham Equations, Chapter 8,\n  pp. 137-152 ( Ed. H.W. Braden and I.M. Krichever, Gordon and Breach,\n  Amsterdam (2000))",
    "title": "Picard-Fuchs Equations, Hauptmoduls and Integrable Systems",
    "url": "https://arxiv.org/abs/solv-int/9902013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bca01d24-3b1c-40b1-946c-2f63846a1363",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}