On the Dynamical Manin-Mumford problem for plane polynomial endomorphisms

Matteo Ruggiero

13-06-2024 - 14:15
Largo Lungo Tevere Dante n 376 - Aula M1


The Dynamical Manin-Mumford problem is a dynamical question inspired by classical results from arithmetic geometry. Given an algebraic dynamical system (X,f), where X is a projective variety and f is a polarized endomorphism on X, we want to determine if a subvariety Y containing "unusually many" periodic points must be itself preperiodic.
In a recent work in collaboration with Romain Dujardin and Charles Favre, we prove this property to hold when f is a regular endomorphism of P^2 coming from a polynomial endomorphism of C^2 of degree d>=2, under the additional condition that the action of f at the line at infinity doesn't have periodic super-attracting points.
We will introduce the problem and some of the ingredients of the proof, coming from arithmetic geometry, holomorphic and non-archimedean dynamics.

org: Turchet Amos