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Rigidity and Height Bounds for Certain Post-critically Finite Endomorphisms of ℙN

  • Patrick Ingram (a1)
Abstract

The morphism f:ℙN→ℙN is called post–critically finite (PCF) if the forward image of the critical locus, under iteration of f, has algebraic support. In the case N = 1, a result of Thurston implies that there are no algebraic families of PCF morphisms, other than a well-understood exceptional class known as the flexible Lattés maps. A related arithmetic result states that the set of PCF morphisms corresponds to a set of bounded height in the moduli space of univariate rational functions. We prove corresponding results for a certain subclass of the regular polynomial endomorphisms of ℙN for any N.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
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