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HEIGHT ESTIMATES FOR DOMINANT ENDOMORPHISMS ON PROJECTIVE VARIETIES

이종규
영남수학회 (Youngnam Mathematical Society)|2016.01|East Asian Mathematical Journal|제32권 제1호|pp. 61-75|DOI http://dx.doi.org/10.7858/eamj.2016.007

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참고문헌

키워드

heightdominant endomorphismNorthcott's theorem
주제분류수학

초록

If φ is a polarizable endomorphism on a projective variety,then the Weil height machine guarantees that φ satis es Northcott's the-orem. In this paper, we show that Northcott's theorem only holds forpolarizable endomorphisms and generalize this result to arbitrary domi-nant endomorphisms: we introduce the height expansion and contractioncoe cients which provide weak Northcott's theorem for dominant endo-morphisms. We also give some applications of the height expansion andcontraction coe cients.

Abstract

If φ is a polarizable endomorphism on a projective variety,then the Weil height machine guarantees that φ satis es Northcott's the-orem. In this paper, we show that Northcott's theorem only holds forpolarizable endomorphisms and generalize this result to arbitrary domi-nant endomorphisms: we introduce the height expansion and contractioncoe cients which provide weak Northcott's theorem for dominant endo-morphisms. We also give some applications of the height expansion andcontraction coe cients.

참고문헌 (23)

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