Algebraic Geometry Seminar: Alon Levy

Suppose that a polarized self-morphism \phi of X dominates a polarized self-morphism \psi of Y. Szpiro and Tucker asked if, if \phi is isotrivial, then \psi also descends to an isotrivial morphism. We give an affirmative answer in a large set of cases, including the case Y = P^1. At heart is a result of Petsche, Szpiro, and Tepper on isotriviality and potential good reduction for self-maps of P^n, which we extend to more general polarized self-morphisms of projective varieties.