East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES

  • Received : 2013.07.31
  • Accepted : 2015.10.25
  • Published : 2016.01.30
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Abstract

If ${\phi}$ is a polarizable endomorphism on a projective variety, then the Weil height machine guarantees that ${\phi}$ satisfies Northcott's theorem. In this paper, we show that Northcott's theorem only holds for polarizable endomorphisms and generalize this result to arbitrary dominant endomorphisms: we introduce the height expansion and contraction coefficients which provide weak Northcott's theorem for dominant endomorphisms. We also give some applications of the height expansion and contraction coefficients.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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