  Given a very ample line bundle on a smooth projective variety, the variation
of Hodge structure associated to the universal family of hyperplane sections
can be thought of as a $D$-module with action generated by the Gauss-Manin
connection. The decomposition theorem for a projective morphism and results
similar to the Lefschetz hyperplane theorem tell us that the only nontrivial
part of this VHS occurs in the middle degree corresponding to the vanishing
cohomology of the hyperplane sections. We use Nori's connectivity theorem to
give an explicit description of the cohomology sheaves of the de Rham complex
of this $D$-module in terms of the vanishing cohomology of the original
variety.
