A bound for the generalized Tjurina numbers

Abstract

We define a series of nonnegative integer valued invariants of an analytic ndimensional isolated complete intersection singularity the generalized Tjurina numbers The Tjurina number is equal to We show that all these numbers are bounded by the Milnor number by establishing explicit formulas for the dierences p involving the mixed Hodge numbers of the cohomology of the link This generalizes earlier results of Looijenga and Steenbrink on the relation between the Milnor number and the Tjurina number For singularities with n among which one nds the weighted homogeneous ones we obtain some purity results for various mixed Hodge structures associated with the singularity and its resolution