Local holomorphic dynamics

seminar: Degree growth of rational surface maps

speaker: Mattias Jonsson (University of Michigan)

abstract: A basic problem of understanding a dynamical system defined by a rational map in (say) two dimensions is to understand the growth of degrees. This problem essentially reduces to linear algebra when the map acts functorially on cohomology, which means that no curve is eventually mapped to an indeterminacy point. When the map is birational, this functorial property can be achieved after blowing up the space finitely many times but it is unknown to what this extent this is possible for noninvertible maps. We circumvent this difficulty by working on the Riemann-Zariski space, an object which can be viewed as the space obtained from the projective plane by blowing up "everything". On the Riemann-Zariski space there are no indeterminacy points and this allows us to at least partially understand the degree growth of the original map.

This is joint work with Sebastien Boucksom and Charles Favre (both at CNRS, France).

timetable:
Wed 24 Jan, 11:20 - 12:20, Aula Dini
<< Go back