Shioda-Tate formula for an abelian fibered variety and applications
Algebraic Geometry
2007-05-23 v1 Number Theory
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\"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.
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Cite
@article{arxiv.math/0703245,
title = {Shioda-Tate formula for an abelian fibered variety and applications},
author = {Keiji Oguiso},
journal= {arXiv preprint arXiv:math/0703245},
year = {2007}
}
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10 pages