Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SHIODA-TATE FORMULA FOR AN ABELIAN FIBERED VARIETY AND APPLICATIONS

  • Oguiso, Keiji (DEPARTMENT OF ECONOMICS KEIO UNIVERSITY, SCHOOL OF MATHEMATICS KOREA INSTITUTE FOR ADVANCED STUDY)
  • Published : 2009.03.31
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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 $hyperk{\ddot{a}}hler$ 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.

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References

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