Residues and filtered \(D\)-modules
Let \(X\) be a smooth projective variety embedded on a sufficiently high degree projective space and consider its dual projective space \(P\). The purpose of this paper is to use residues to define a filtered regular holonomic \(\mathcal{D}\)-module \((\mathcal{M}, F)\) on \(P\) that provides 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 \(X\).'' Besides the theoretical value of the description provided by the filtered \(\mathcal{D}\)-modules constructed, there is also practical interest in the results of this paper since the good properties presented by the sheaves \(F_k\mathcal{M}\), such as positivity or reflexivity, can translated in correspondent analytic spaces, namely as holomorphic convexity or control over singularities. For these reasons (presented here in a very synthetic way) we consider that this work is an important contribute for \(\mathcal{D}\)-module theory.
filtered regular holonomic \(\mathcal{D}\)-module
scientific article; zbMATH DE number 6087545
scientific article