A Bound for the Generalized Tjurina Numbers
نویسندگان
چکیده
We deene a series of non-negative integer valued invariants (1) of an analytic n-dimensional isolated complete intersection singularity (the generalized Tjurina numbers). The Tjurina number is equal to (1). We show that all these numbers are bounded by the Milnor number by establishing explicit formulas for the diierences ? (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 = (1) = = (n?1) (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.
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