On the hard Lefschetz theorem in intersection homology for complex varieties with isolated singularities
type: Item
instance of: scholarly article
title: On the hard Lefschetz theorem in intersection homology for complex varieties with isolated singularities
zbMATH Open document ID: 0648.14009
DOI: 10.1007/BF01830675
author: Karl-Heinz Fieseler
author: Ludger Kaup
published in: Aequationes Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137243
review text: Let X be a complex projective algebraic variety of pure complex dimension n, Z a transversal hypersurface section, \({\mathfrak p}\leq {\mathfrak q}\) two perversities and R a principal ideal domain. The author discusses the homomorphisms induced by the intersection product with \(Z^ k\) on the intersection homologies \(L^ k({\mathfrak p},{\mathfrak q}): I_{{\mathfrak p}}H_{n+k}(X,R)\to I_{{\mathfrak q}}H_{n-k}(X,R)\) where X has only isolated singularities. He first studies the Lefschetz and Gysin homomorphisms in any codimension. He then proves different cases, depending on the characteristic of R, where \(L^ k({\mathfrak p},{\mathfrak q})\) are bijective or injective using the corresponding Gysin homomorphisms.
Mathematics Subject Classification ID: 14F99
Mathematics Subject Classification ID: 14C17
zbMATH DE Number: 4057663
zbMATH Keywords: hard Lefschetz theorem
zbMATH Keywords: intersection homologies
zbMATH Keywords: Gysin homomorphisms
reviewed by: Aigli Papantonopoulou
MaRDI profile type: Publication
cites work: Q4189377
cites work: Q3320507
cites work: Intersection homology theory
cites work: Intersection homology. II
cites work: Linking pairings on singular spaces
cites work: Q3039482
cites work: Q3051109
cites work: Partial Poincaré duality for k-regular spaces and complex algebraic sets
cites work: Q3669555
cites work: The topology of complex projective varieties after S. Lefschetz
cites work: Q3737541
cites work: Isolated singularities of algebraic surfaces with \(\mathbb{C}^{*}\) action
cites work: Q3661709
OpenAlex ID: W2059029183
Recommended article: Q3474756
Recommended article: Q4941098
Recommended article: Q3731745
Recommended article: Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes
Recommended article: The Hodge structures on the intersection homology of varieties with isolated singularities
Recommended article: \(L_ 2\)-cohomology and intersection homology of certain algebraic varieties with isolated singularities
Recommended article: Hard Lefschetz properties and distribution of spectra in singularity theory and Ehrhart theory
Recommended article: Q4664553
Recommended article: Hard Lefschetz theorem for Vaisman manifolds
Recommended article: Q3973870
description: scientific article; zbMATH DE number 4057663