Speaker: Ben Hutz (Saint Louis U.)

Title: A bound on the periodic part of the forward orbit of a projective subvariety

Abstract: Let $f:mathbb{P}^N to mathbb{P}^N$ be a morphism and $X subseteq mathbb{P}^N$ a (projective) variety. We obtain a bound on the periodic part of the forward orbit of $X$ by examining the orbit modulo a prime of good reduction. This bound depends only on the degree of the map, the degree of the subvariety, the dimension of the projective space, the degree of the number field, and the prime of good reduction.

This talk will be split into two different cases. First, a review of the case when $dim(X) = 0$, i.e., iteration of points. For the projective line, a series of results due to Li, Morton-Silverman, Narkiewicz, Pezda, and Zieve provide the main theorem. This was generalized by the speaker in 2009 to any $N$. Second, the main part of the talk describes the speaker’s new result for the case $dim(X) > 0$.