Picard-Lefschetz theory for the universal coverings of complements to affine hypersurfaces
type: Item
instance of: scholarly article
title: Picard-Lefschetz theory for the universal coverings of complements to affine hypersurfaces
zbMATH Open document ID: 0928.14011
author: Ichiro Shimada
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2000-01-20T00:00:00Z
review text: Summary: We study the global monodromy on the middle homology group of the universal coverings of the complements to non-singular affine hypersurfaces which intersect the hyperplane at infinity transversely. This monodromy can be regarded as a deformation of the monodromy on the middle homology group of the affine hypersurfaces. We show that this representation becomes irreducible when the deformation parameter is generic.
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 32S55
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 1038657
zbMATH Keywords: Picard-Lefschetz theory
zbMATH Keywords: universal coverings
zbMATH Keywords: complements to non-singular affine hypersurfaces
zbMATH Keywords: deformation of the monodromy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195162384
OpenAlex ID: W1992303732
cites work: Q3973295
cites work: Théorie de Hodge. II. (Hodge theory. II)
cites work: Q3934511
cites work: On the fundamental group of the complement of a node curve
cites work: Q3943065
cites work: Twisted Picard-Lefschetz formulas
cites work: The topology of complex projective varieties after S. Lefschetz
cites work: Q3320506
cites work: Homotopy groups of the complements to singular hypersurfaces. II
cites work: Formules de Picard-Lefschetz généralisées et ramification des intégrales
cites work: A theorem on the Poincaré group of an algebraic hypersurface
DOI: 10.2977/PRIMS/1195162384
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description: scientific article; zbMATH DE number 1038657