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Du Bois invariants of isolated complete intersection singularities. (English) Zbl 0889.32035
Let \((X,x)\) be a pure \(n\)-dimensional isolated singularity and \(\pi:(Y,E) \to (X, x)\) a good resolution \((E\) is a divisor with normal crossings on \(Y)\). The Du Bois invariants are defined by \[ b^{p,q} (X,x)= \dim H^q \bigl(Y,\Omega^p_Y (\log E) (-E) \bigr). \] They do not depend on the choice of the resolution.
The article starts with a survey about known properties of these invariants. The relation to the Hodge numbers of the local and vanishing cohomology groups is given. It is proved that the Tjurina number of certain Gorenstein singularities can be expressed in terms of Du Bois invariants and Hodge numbers of the link. Similarly it is done for the Hodge numbers of the Milnor fibre of certain three-dimensional complete intersections.

MSC:
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
32S05 Local complex singularities
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References:
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