Généralisation d'une formule de Katz-Steenbrink. (Generalization of a Katz-Steenbrink formula) (Q1075394)

Let \(f:\quad X\to D\) be a proper map from an analytic variety X onto the unit disk D such that \(Y=f^{-1}(0)\) has normal crossings and let V be a local system on \(X\setminus Y\). The aim of the present paper is to prove that \(R\psi\) V, the ''complex of vanishing cycles of V'' is quasi- isomorphic to a certain complex constructed by means of differentials. This generalizes a result due to Katz-Steenbrink [see \textit{J. Steenbrink}, Invent. Math. 31, 229-257 (1976; Zbl 0303.14002)].