Degree gaps for multipliers and the dynamical Andre-Oort conjecture (2007.00567v2)

Abstract: We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multiplier of very low degree, except those which vanish, generalizing results of Baker and DeMarco, and Favre and Gauthier.