Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
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计算椭圆三重的 Mordell-Weil 秩和奇异超曲面的上同调
DOI：
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发表时间：
2008
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影响因子：
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通讯作者：
R. Kloosterman
中科院分区：
文献类型：
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作者：
K. Hulek;R. Kloosterman
本文给出了二元有理函数域上一般椭圆曲线的秩的一种计算方法。我们把这个问题归结为计算加权射影四维空间中奇异超曲面的上同调。然后给出了一类奇异超曲面的上同调的计算方法，推广了Dimca在孤立奇异情形下的工作。
In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective 4-space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.