The perverse filtration and the Lefschetz hyperplane theorem
type: Item
instance of: scholarly article
title: The perverse filtration and the Lefschetz hyperplane theorem
zbMATH Open document ID: 1213.14017
author: Mark Andrea A. de Cataldo
author: Luca Migliorini
published in: Annals of Mathematics. Second Series
publication date: 2010-05-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/0805.4634
full work available at URL: p14.xhtml
review text: Let \(Y\) be a quasi-projective variety and \(K\) be a \(\Sigma\)-constructible complex on \(Y\) with respect to a given stratification \(\Sigma\) of \(Y\). The theory of \(-\)structures endows the hypercohomology groups \(H(Y,K)\) with the so-called perverse filtration \(P^pH(Y,K)\). Given a sequence \(Y\supset Y_{-1}\supset\dots\supset Y_{-n}\) of closed subvarieties of \(Y\), called an \(n\)-flag, basic sheaf theory endows \(H(Y,K)\) with the so-called flag filtration given by \[ F^pH(Y,K)= \text{Ker}(H(Y,K)\to H(Y_{p-2},K|_{y_{p-1}}). \] The main result of this paper is that if the \(n\)-flag is obtained using \(n\) hyperplanes in sufficiently general position, then these two filtrations coincide: \[ P^pH^j(Y,K)= F^{p+j}H^j(Y,K). \]
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14D07
Mathematics Subject Classification ID: 14Gxx
Mathematics Subject Classification ID: 14Fxx
zbMATH DE Number: 5712769
reviewed by: Xi Chen
MaRDI profile type: Publication
OpenAlex ID: W2570499741
arXiv ID: 0805.4634
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DOI: 10.4007/ANNALS.2010.171.2089
description: scientific article