Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces

@article{Hulek2008CalculatingTM,
  title={Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces},
  author={Klaus Hulek and Remke Kloosterman},
  journal={arXiv: Algebraic Geometry},
  year={2008}
}
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. 
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