An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: Recent Developments

Monodromy preserving deformations of the linear differential equations on elliptic curves and the sixth Painleve equation

Author: Toshiyuki Mano (Kyoto University)

Abstract

We shall study behaviours of the monodromy preseving deformation equations on elliptic curves when the elliptic curves degenerate to a rational curve with an ordinary double point. We shall also formulate monodromy preserving deformations on the rational curve with an ordinary double point and identify this equation and above degenerated Hamiltonian system. Then we relate solutions of monodoromy preserving deformation equation to solutions of the sixth painleve equation through the process of resolution of singularity on the rational curve.