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Shioda-Tate formula for an abelian fibered variety and applications

Keiji Oguiso
대한수학회 (The Korean Mathematical Society)|2009.03|대한수학회지 (Journal of the KMS)|제46권 제2호|pp. 237-248

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참고문헌

키워드

Mordell-Weil group
주제분류수학

초록

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered hyperkähler manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

Abstract

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered hyperkähler manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

참고문헌 (24)

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