A finiteness result for post-critically finite polynomials

2010/10/17 by Ingram, Patrick · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1010.3393

Abstract

We show that the set of complex points in the moduli space of polynomials of degree d corresponding to post-critically finite polynomials is a set of algebraic points of bounded height. It follows that for any B, the set of conjugacy classes of post-critically finite polynomials of degree d with coefficients of algebraic degree at most B is a finite and effectively computable set. In the case d=3 and B=1 we perform this computation. The proof of the main result comes down to finding a relation between the "naive" height on the moduli space, and Silverman's critical height.

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