A Dynamical Variant of the André-Oort Conjecture

Abstract In the moduli space $\mathrm{MP}_d$ of degree $d$ polynomials, special subvarieties are those cut out by critical orbit relations, and then special points are the post-critically finite polynomials. It was conjectured that in $\mathrm{MP}_d$, subvarieties containing a Zariski-dense set of s...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2018-04, Vol.2018 (8), p.2447-2480
Main Authors: Ghioca, Dragos, Ye, Hexi
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Abstract In the moduli space $\mathrm{MP}_d$ of degree $d$ polynomials, special subvarieties are those cut out by critical orbit relations, and then special points are the post-critically finite polynomials. It was conjectured that in $\mathrm{MP}_d$, 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 $d=3$.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnw314