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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2009; 46(2): 237-248

Printed March 1, 2009

Copyright © The Korean Mathematical Society.

Shioda-Tate formula for an abelian fibered variety and applications

Keiji Oguiso

Keio University

Abstract

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We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered hyperk\"ahler 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.

Keywords: Mordell-Weil group

MSC numbers: 14C22, 14D06, 14J28, 14J40

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