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Interaction of consecutive strata for vanishing cycles. (Interaction de strates consécutives pour les cycles évanescents.) (French) Zbl 0772.32024
Let \(f:X\to\mathbb{C}\) be holomorphic, \(X\subseteq\mathbb{C}^{n+1}\) open, connected and Stein containing 0 and \(Y=f^{-1}(0)\).
Denote by \(H^ p\) the constructible sheave 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 \(e^{-2\pi iu}\) of the monodromy denote by \(H^ p(u)\) the corresponding subsheave.
The author studies \(H^ n(u)\) and \(H^{n-1}(u)\) under the following assumptions:
\(H^ n(u)\) is concentrated at 0.
\(H^{n-1}(u)\) is concentrated on a curve \(S\) having 0 as unique singular point.
\(H^{n-1}(u)| S-\{0\}\) is a local system.
\(H^ i(u)=0\) if \(i\leq n-2\).
One of the main results is an analytic formula for the hermitic intersection form on \(H^ n(u)\) via meromorphic continuation of the distribution \(\int_ X| f|^{2\lambda}\).
Reviewer: G.Pfister (Berlin)

MSC:
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
32S55 Milnor fibration; relations with knot theory
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