Calculating the Mordell-Weil rank of elliptic threefolds and the   cohomology of singular hypersurfaces
  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. 
Klaus Hulek and Remke Kloosterman