The Dynamical Andre-Oort Conjecture for cubic polynomials

2016/03/16 by Dragos Ghioca, Ghioca, Dragos, Hexi Ye +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Coding theory and cryptography #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1603.05303

openalex publication_date 2016/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Torsion points on families of squares of elliptic curves

Cited by

• Activity measures of dynamical systems over non-archimedean fields

Related

• A case of the Dynamical Andre-Oort Conjecture
• Special curves and postcritically-finite polynomials
• Degree gaps for multipliers and the dynamical Andre-Oort conjecture
• The arithmetic of polynomial dynamical pairs
• Combinatorial models for spaces of cubic polynomials