Picard-Fuchs Equations, Hauptmoduls and Integrable Systems

J. Harnad

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Picard-Fuchs Equations, Hauptmoduls and Integrable Systems

J. Harnad

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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 Painlevé VI equations.

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solv-int hep-th math-ph math.AG math.GR math.MP math.NT nlin.SI

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BibTeX RIS

J. Harnad. 1999-02-18. Picard-Fuchs Equations, Hauptmoduls and Integrable Systems. https://arxiv.org/abs/solv-int/9902013

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