Picard-Fuchs Equations, Hauptmoduls and Integrable Systems

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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 Painlevé VI equations.
PlainTeX 15gs. Write - up of lecture given at international meeting: Integrability: Seiberg-Witten and Witham Equations, ICMS, Edinburgh, September 14-19, 1998

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Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Mathematical Physics, Algebraic Geometry, Group Theory, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/94498

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/solv-int/9902013
 http://arxiv.org/abs/solv-int/9902013
 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))

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arXiv