Picard-Fuchs Equations, Hauptmoduls and Integrable Systems

Details Picard-Fuchs Equations, Hauptmoduls and Integrable Systems Picard-Fuchs Equations, Hauptmoduls and Integrable Systems

1999-02-18

arxiv.org/abs/solv-int/9902013v1

Integrability: The Seiberg-Witten and Witham Equations, Chapter 8, pp. 137-152 ( Ed. H.W. Braden and I.M. Krichever, Gordon an

Physics

High Energy Physics

High Energy Physics - Theory

PlainTeX 15gs. Write - up of lecture given at international meeting: Integrability: Seiberg-Witten and Witham Equations, ICMS,

Scientific paper

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.

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