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arXiv · 1603.05303

The Dynamical Andre-Oort Conjecture for cubic polynomials

Dragos Ghioca·Hexi Ye
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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.

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Dragos Ghioca, Hexi Ye. 2016-03-16. The Dynamical Andre-Oort Conjecture for cubic polynomials. https://arxiv.org/abs/1603.05303

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