The Dynamical Andre-Oort Conjecture for cubic polynomials
Number Theory
2016-03-18 v1 Algebraic Geometry
Dynamical Systems
Abstract
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 polynomials. It was conjectured that in the moduli space of degree d polynomials, the subvarieties containing a Zariski-dense set of special points are exactly these special subvarieties. In this article, we prove the first non-trivial case for this conjecture: the case of cubic polynomials.
Cite
@article{arxiv.1603.05303,
title = {The Dynamical Andre-Oort Conjecture for cubic polynomials},
author = {Dragos Ghioca and Hexi Ye},
journal= {arXiv preprint arXiv:1603.05303},
year = {2016}
}
Comments
At the time we were finishing writing this article, we learned that Charles Favre and Thomas Gauthier have independently obtained a proof of our main theorem using a different approach; we are grateful to both of them for sharing with us their preprint