The Medvedev-Scanlon Conjecture for Semiabelian Varieties and certain 3-folds

Thursday, October 12, 2017 - 1:00pm
MSB 110
Matt Satriano

The Medvedev-Scanlon conjecture predicts when an algebraic dynamical system has a rational point with dense orbit. Specifically, if $X$ is a projective variety and $f\colon X\dasharrow X$ is dominant rational map, it states that such a rational point exists precisely when $f$ does not preserve a fibration. In work with Ghioca, we prove the conjecture for regular morphisms $f$ of semiabelian varieties. We discuss this result as well as joint work with Bell, Ghioca, and Reichstein where we handle several classes of 3-folds contingent on certain conjectures in the Minimal Model Program.