Abstract
For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic \({\mathcal{D}}\) -module \({(\mathcal{M}, F)}\) on the dual projective space. This gives a concrete description of the intermediate extension to a Hodge module on P of the variation of Hodge structure on the middle-dimensional cohomology of the hyperplane sections of X. We also establish many results about the sheaves \({F_k{\mathcal{M}}}\) , such as positivity, vanishing theorems, and reflexivity.
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