Laura DeMarco : Geometry and algebra of preperiodic points in PN - Lecture 3 скачать в хорошем качестве

Laura DeMarco : Geometry and algebra of preperiodic points in PN - Lecture 3

In these lectures, we will examine a series of conjectures about the geometry of preperiodic points for endomorphisms of $ \mathbb{P}^{N}$. Lecture 1 will focus on the Dynamical ManinMumford Conjecture (DMM), formulated by Shouwu Zhang in the 1990s as an extension of the well-known Manin-Mumford Conjecture (which investigated the geometry of torsion points in abelian varieties and was proved in the early 1980s by Raynaud). The DMM aims to classify the subvarieties of $\mathbb{P}^{N}$ containing a Zariski-dense set of preperiodic points. Lectures 2 and 3 will be devoted to conjectures that treat families of maps on $\mathbb{P}^{N}$. One conjecture in particular was inspired by the recently-proved ”Relative Manin-Mumford” theorem of Gao-Habegger for abelian varieties, but the dynamical version turns out to be closely related to the study of dynamical stability and to contain many previously-existing questions/conjectures/results about moduli spaces of maps on $\mathbb{P}^{N}$. These lectures are based on joint work with Myrto Mavraki. CONFERENCE Recording during the thematic meeting : «Arithmetic, Algebraic and Analytics Dynamics » the January 21, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area