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http://dx.doi.org/10.7858/eamj.2016.007

HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES  

Lee, Chong Gyu (Department of Mathematics, Soongsil University)
Publication Information
East Asian mathematical journal / v.32, no.1, 2016 , pp. 61-75 More about this Journal
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
height; dominant endomorphism; Northcott's theorem;
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Times Cited By KSCI : 1  (Citation Analysis)
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