Canonical height functions for monomial maps

Jan Li Lin*, Chi Hao Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The height function measures the arithmetic complexity of a point on a variety over ℚ. The canonical height function measures the asymptotic height growth (relative to the degree growth) of a point under a dominant rational map. One property desired for the canonical height function is the Northcott finiteness property, which states that there are only finitely many points for a bounded degree and a bounded height. We show that the canonical height function for dominant rational maps does not have the Northcott finiteness property in general. We develop a new canonical height function for monomial maps. In certain cases, this new canonical height function has the desired nice properties.

Original languageEnglish (US)
Pages (from-to)1821-1840
Number of pages20
JournalInternational Journal of Number Theory
Volume9
Issue number7
DOIs
StatePublished - Nov 2013

Keywords

  • Canonical height functions
  • Monomial maps
  • Northcott finiteness property

ASJC Scopus subject areas

  • Algebra and Number Theory

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