On the hard Lefschetz theorem in intersection homology for complex varieties with isolated singularities (Q1104993)

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.