Monodromy of variations of Hodge structure
type: Item
instance of: scholarly article
title: Monodromy of variations of Hodge structure
zbMATH Open document ID: 1079.14017
DOI: 10.1023/A:1022344213544
author: Chris Peters
author: Jozef Steenbrink
published in: Acta Applicandae Mathematicae
publication date: 2003-04-27T00:00:00Z
review text: The \(k\)th primitive cohomology group \(H^k_{\text{prim}}(X)\) of a smooth projective variety \(X\) is known to carry a weight \(k\) polarized rational Hodge structure. For a family of those over a smooth connected base manifold \(S\), the cohomology groups glue together to a local system on \(S\). Such a local system is completely determined by its monodromy representation, i.e. the induced representation of \(\pi _1(S,s_0)\) on the \(k\)th cohomology group \(V\) of the fibre at \(s_0\). The authors present a survey of properties of the monodromy of local systems on quasi-projective varieties which underlie a variation of a Hodge structure. They also discuss a less widely known version of a Noether-Lefschetz-type theorem.
Mathematics Subject Classification ID: 14D07
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 32G20
zbMATH DE Number: 1901299
zbMATH Keywords: variation of a Hodge structure
zbMATH Keywords: monodromy group
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: a:1022344213544
OpenAlex ID: W153673774
description: scientific article; zbMATH DE number 1901299