Residues and filtered \(D\)-modules
type: Item
instance of: scholarly article
title: Residues and filtered \(D\)-modules
zbMATH Open document ID: 1251.14006
author: Christian Schnell
published in: Mathematische Annalen
publication date: 2012-09-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1005.0543
review text: 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.
reviewed by: Ana Rita Martins
Mathematics Subject Classification ID: 14D07
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 14D10
zbMATH DE Number: 6087545
zbMATH Keywords: filtered regular holonomic \(\mathcal{D}\)-module
zbMATH Keywords: variation of Hodge structures
MaRDI profile type: Publication
OpenAlex ID: W2043166053
arXiv ID: 1005.0543
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DOI: 10.1007/S00208-011-0746-0
description: scientific article; zbMATH DE number 6087545