Abstract: 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.
Il seminario si svolgerà in presenza nell'aula M1. Per ulteriori informazioni, si può contattare gli organizzatori all'email amos.turchet@uniroma3.it.
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