A rational map with infinitely many points of distinct arithmetic degrees

John Lesieutre; Matthew Satriano

doi:10.1017/etds.2019.30

A rational map with infinitely many points of distinct arithmetic degrees

John Lesieutre
, Matthew Satriano

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let be a dominant rational self-map of a smooth projective variety defined over. For each point whose forward -orbit is well defined, Silverman introduced the arithmetic degree, which measures the growth rate of the heights of the points. Kawaguchi and Silverman conjectured that is well defined and that, as varies, the set of values obtained by is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when.

Original language	English (US)
Pages (from-to)	3051-3055
Number of pages	5
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	11
DOIs	https://doi.org/10.1017/etds.2019.30
State	Published - Nov 1 2020

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1017/etds.2019.30

Cite this

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A rational map with infinitely many points of distinct arithmetic degrees

Abstract

All Science Journal Classification (ASJC) codes

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