Johannes Duistermaat, Universiteit Utrecht

QRT and elliptic surfaces

A QRT map is a rational map from a plane to itself which is defined by a pencil of biquadratic curves. Each smooth biquadratic curve is an elliptic curve, on which the map acts as a translation. Blowing up the plane at the base points, the points through which all the curves pass starlike, one obtains a rational elliptic surface, on which the QRT map acts as a genuine automorphism.
The curves form a fibration of the surface, where singular fibers do occur, and even the regular fibers are not isomorphic to each other. One of the goals of the course is to show how many aspects of the situation can be computed explicitly.