• Title/Summary/Keyword: dominant endomorphism

Search Result 1, Processing Time 0.014 seconds

HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES

  • Lee, Chong Gyu
    • East Asian mathematical journal
    • /
    • v.32 no.1
    • /
    • pp.61-75
    • /
    • 2016
  • 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.