Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HEIGHT INEQUALITY FOR RATIONAL MAPS AND BOUNDS FOR PREPERIODIC POINTS

  • Received : 2016.01.25
  • Accepted : 2018.06.12
  • Published : 2018.09.30
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Abstract

In this paper, we introduce the D-ratio of a rational map $f:{\mathbb{P}}^n{\dashrightarrow}{\mathbb{P}}^n$, defined over ${\bar{\mathbb{Q}}}$, whose indeterminacy locus is contained in a hyperplane H on ${\mathbb{P}}^n$. The D-ratio r(f; ${\bar{V}}$) characterizes endomorphisms and provides a useful height inequality on ${\mathbb{P}}^n({\bar{\mathbb{Q}}}){\backslash}H$. We also provide a dynamical application: preperiodic points of dynamical systems of small D-ratio are of bounded height.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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