dorsal/arxiv
View SchemaPicard-Fuchs Equations, Hauptmoduls and Integrable Systems
| Authors | J. Harnad |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9902013 |
| URL | https://arxiv.org/abs/solv-int/9902013 |
| Journal | Integrability: The Seiberg-Witten and Witham Equations, Chapter 8, pp. 137-152 ( Ed. H.W. Braden and I.M. Krichever, Gordon and Breach, Amsterdam (2000)) |
Abstract
The Schwarzian equations satisfied by certain Hauptmoduls (i.e., uniformizing functions for Riemann surfaces of genus zero) are derived from the Picard-Fuchs equations for families of elliptic curves and associated surfaces. The inhomogeneous Picard-Fuchs equations associated to elliptic integrals with varying endpoints are derived and used to determine solutions of equations that are algebraically related to a class of Painlev\'e VI equations.
{
"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
}