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

Details 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

2008-06-12

arxiv.org/abs/0806.2025v3

Mathematics

Algebraic Geometry

Revised paper; final section is shortened; correction of typos

Scientific paper

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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