27 citations · 83 across the 13 of their papers we have counts for
6 papers · 1 filter
Uniform Manin-Mumford for a family of genus 2 curves
Laura DeMarco, Holly Krieger, Hexi Ye
We introduce a general strategy for proving quantitative and uniform bounds on the number of common points of height zero for a pair of inequivalent height functions on $\mathbb{P}…
The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for endomorphisms of (P^1)^n
Dragos Ghioca, Khoa D. Nguyen, Hexi Ye
We prove Zhang's Dynamical Manin-Mumford Conjecture and Dynamical Bogomolov Conjecture for dominant endomorphisms of (P^1)^n. We use the equidistribution theorem for points of smal…
Bounded height in families of dynamical systems
Laura DeMarco, Dragos Ghioca, Holly Krieger +3
Let a and b be algebraic numbers such that exactly one of a and b is an algebraic integer, and let f_t(z):=z^2+t be a family of polynomials parametrized by t. We prove that the set…
The Dynamical Andre-Oort Conjecture for cubic polynomials
Dragos Ghioca, Hexi Ye
In the moduli space of degree d polynomials, the special subvarieties are those cut out by critical orbit relations, and then the special points are the post-critically finite poly…
The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps
Dragos Ghioca, Khoa D. Nguyen, Hexi Ye
We prove the Dynamical Bogomolov Conjecture for endomorphisms of P^1\times P^1 defined over a number field. We use the equidistribution theorem for points of small height with resp…
Finiteness of commutable maps of bounded degree
Chong Gyu Lee, Hexi Ye
In this paper, we study the relation between two dynamical systems (V,f) and (V,g) with f. g = g . f. As an application, we show that an endomorphism (respectively a polynomial map…