Rigidity and Height Bounds for Certain Post-critically Finite Endomorphisms of ℙN
2016 ◽
Vol 68
(3)
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pp. 625-654
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AbstractThe 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.
2003 ◽
Vol 47
(1)
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pp. 1-20
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2010 ◽
Vol 14
(06)
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pp. 141-153
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2018 ◽
Vol 51
(3)
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pp. 739-772
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2017 ◽
Vol 50
(5)
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pp. 1081-1122
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1999 ◽
Vol 105
(1-2)
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pp. 285-297
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