HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES

Title & Authors
HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES
Lee, Chong Gyu;

Abstract
If $\small{{\phi}}$ is a polarizable endomorphism on a projective variety, then the Weil height machine guarantees that $\small{{\phi}}$ satisfies Northcotts theorem. In this paper, we show that Northcotts 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 Northcotts theorem for dominant endomorphisms. We also give some applications of the height expansion and contraction coefficients.
Keywords
height;dominant endomorphism;Northcotts theorem;
Language
English
Cited by
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