# 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.

#### 28 Citations

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Defect formula for nodal complete intersection threefolds

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In this paper, we give formulas for the Hodge numbers of a nodal complete intersection in a complex projective space. We apply these formulas to construct examples of Calabi–Yau threefolds with…

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We show that the degree of the Alexander polynomial of an irreducible plane algebraic curve with nodes and cusps as the only singularities does not exceed 5 3 d−2 where d is the degree of the curve.…

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We describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant $j$-invariant. Moreover, we classify all such elliptic threefolds if the $j$-invariant is…

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