Picard-Fuchs Equations, Hauptmoduls and Integrable Systems
solv-int
2007-05-23 v1 High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Group Theory
math.MP
Number Theory
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.solv-int/9902013,
title = {Picard-Fuchs Equations, Hauptmoduls and Integrable Systems},
author = {J. Harnad},
journal= {arXiv preprint arXiv:solv-int/9902013},
year = {2007}
}
Comments
PlainTeX 15gs. Write - up of lecture given at international meeting: Integrability: Seiberg-Witten and Witham Equations, ICMS, Edinburgh, September 14-19, 1998