Interaction of consecutive strata. II (Q2386885)

The article completes the results of the author [\textit{D. Barlet}, Ann. Sci. Éc. Norm. Supér. (4) 24, 401--506 (1991; Zbl 0772.32024)]. Let \(f:X\to \mathbb C\) be holomorphic, \(X\subseteq\mathbb C^{n+1}\) open, connected and Stein containing \(0\) and \(Y=f^{-1}(0)\). Let \(H^p\) be the sheaves on \(Y\) having as fibres in \(x\in Y\) the \(p\)-th cohomology group with complex coefficients of the Milnor fibre of \(f\) in \(x\). For an eigenvalue \(e^{-2\pi i u}\) of the monodromy let \(H^p(u)\) be the corresponding subsheaf. The so-called tangling phenomenon for a given cohomology class of the Milnor fibre of \(f\) at the origin is studied in case where its nilpotency order for the given eigenvalue \(e^{-2\pi i u} \neq \;1\) is not necessarily bigger or equal than the nilpotency order of the monodromy for this eigenvalue at a generic point of the big stratum. It is proved that this tangling phenomenon can always be detected on the poles of the meromorphic extensions of the distribution \(\int_X| f| ^{2\lambda}\;\square\).