Hypercohomology of Milnor fibres (Q1922757)

The hypercohomology of Milnor fibres with coefficients in bounded, constructible complexes of sheaves is described. Let \(X\) be an analytic space, \(F^\bullet\) a bounded, constructible complex of sheaves on \(X\), \(f : X \to \mathbb{C}\) a complex analytic function with a stratified isolated critical point \(x \in X\), then the relative hypercohomology, with coefficients in \(F^\bullet\) of a small ball around \(x\) modulo the Milnor fibre of \(f\) at \(x\) is a direct sum of powers of the hypercohomology of the normal data to each of the strata. The exponents occurring in this sum are explicitly calculated. The general case of a stratified critical locus of arbitrary dimension is also studied. As an application the formula of Greuel and Lê for the Milnor number of isolated complete intersections is generalized.