Speaker: Laura DeMarco, Harvard University
January 12, 2024 09:00 AM
- 10:00 AM
Abstract:
We will look at the (algebraic) geometry of periodic and preperiodic points in families of maps on PN and present a conjectural characterization of subvarieties containing many of them. (More precisely, if the family is parameterized by a complex algebraic variety S, we aim to describe subvarieties of S x PN that arise as the Zariski-closure of some infinite subset of preperiodic points.) The characterization will be formulated in terms of a dynamically-defined current in S x PN. This is work in progress with Myrto Mavraki, inspired by recent theorems of Gao-Habegger and others on families of abelian varieties. In this dynamical context, there are interesting connections to the theory of J-stability in families and questions about parameter~spaces.