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Given a very ample line bundle on a smooth projective variety, the variationof Hodge structure associated to the universal family of hyperplane sectionscan be thought of as a $D$-module with action generated by the Gauss-Maninconnection. The decomposition theorem for a projective morphism and resultssimilar to the Lefschetz hyperplane theorem tell us that the only nontrivialpart of this VHS occurs in the middle degree corresponding to the vanishingcohomology of the hyperplane sections. We use Nori's connectivity theorem togive an explicit description of the cohomology sheaves of the de Rham complexof this $D$-module in terms of the vanishing cohomology of the originalvariety.

Nori's connectivity theorem from the perspective of $D$-modules