Bifurcations, intersections, and heights

By Laura Demarco. 2014

56 citations recorded by the source corpus.

In this article, we prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for algebraic families of rational maps $f_t: \mathbb{P}^1(\mathbb{C}) \to \mathbb{P}^1(\mathbb{C})$, parameterized by $t$ in a quasi-projective complex variety. We use this to prove one implication in the if-and-only-if statement of Conjecture 1.10 in [Baker-DeMarco, 2013] on unlikely intersections in the moduli space of rational maps; we present the conjecture here in a more general form.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/843418f961d661dba935df2cabe828bfac5323bd

Citations in the corpus

• Current trends and open problems in arithmetic dynamics (2018, unknown): “3 (Ghioca–Hsia–Tucker, 2013; [88]; DeMarco, 2016, [54]).”