The paper introduces a spectral sequence calculating integer homology of the image of a stable perturbation \(f\) of a holomorphic map-germ \(\mathbb{C}^ n \to \mathbb{C}^ p\), \(n < p\). The \(E^ 1\) term of the sequence is formed by the homology of complexes of alternating chains on the multiple point sets \(D^ k\) \((D^ k\) is a closure, in \((\mathbb{C}^ n)^ k\), of the set of \(k\)-tuples of pairwise distinct points sharing the same image under \(f\); “alternating” means “anti-symmetric with respect to the natural action of the \(k\)th permutation group”). For map-germs of corank 1 the spectral sequence degenerates at \(E^ 1\). This follows from a vanishing type theorem for certain twisting homology of Milnor fibres of isolated complete intersection singularities (this theorem is a basic technical result of the paper). Similar spectral sequence exists for discriminants of map-germs \(\mathbb{C}^ n \to \mathbb{C}^ p\), \(n \geq p\). All these results are extensions of the results of the author and D. Mond [Compos. Math. 89, No. 1, 45-80 (1993)] for rational cohomology of images.
Real representations of complex links of some Weyl groups are also discussed.