## Monodromy and weight filtration for smoothings of isolated singularities.(English)Zbl 0844.14001

Given a germ of a flat smoothing deformation of an isolated singularity of a complex variety, the author describes the weighted filtration of the limit mixed Hodge structure in the mean vanishing cohomology of a smooth generic fiber, generated by a logarithm of the unipotent part of the monodromy transformation around the critical value. In particular, it is given a formula for the signature of the intersection form via the Hodge numbers of the vanishing cohomology. This completes the results of the author’s earlier work [Proc. Symp. Pure Math. 40, Part 2, 513-536 (1983; Zbl 0515.14003)].

### MSC:

 14B05 Singularities in algebraic geometry 32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects) 14D07 Variation of Hodge structures (algebro-geometric aspects)

Zbl 0515.14003
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### References:

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