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Minimally critical endomorphisms of P^N

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arxiv 2006.12869 v3 pith:7FHZ77VZ submitted 2020-06-23 math.NT math.DS

Patrick Ingram This is my paper · ORCID
classification math.NTmath.DS
keywords criticalheightspacecasecomparableconfirmingconjecturedefined
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We study the dynamics of the map endomorphism of N-dimensional projective space defined by f(X)=AX^d, where A is a matrix and d is at least 2. When d>N^2+N+1, we show that the critical height of such a morphism is comparable to its height in moduli space, confirming a case of a natural generalization of a conjecture of Silverman.

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  1. Heights and morphisms in number fields

    math.NT 2024-11 conditional novelty 8.0 of 10

    Provides an explicit power-saving asymptotic for counting points by pullback height under morphisms between projective spaces over number fields.

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