Cubic Pencils and Painlevé Hamiltonians

Abstract

We present a simple heuristic method to derive the Painlevé differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.

9 pages with 1 figure in EPS

Cited by in corpus (2)

• Symmetries of quantum Lax equations for the Painlevé equations
• Uniform convergence of hypergeometric series