# zbMATH — the first resource for mathematics

The mixed Hodge structure of a complete intersection with isolated singularity. (English. Abridged French version) Zbl 0861.14007
From the abstract: Consider a deformation $$g$$ of a complete intersection with isolated singularity and with discriminant $$\Delta$$. Assume that $$\Delta$$ is a divisor with normal crossings, and let $$G$$ be the fundamental group of its local complement. We announce the proof of the existence of a mixed Hodge structure on the vanishing cohomology of $$g$$ compatible with the action of $$G$$, and of its equivariant decomposition in polarized mixed Hodge structures. Moreover, we find the local analog of Cattani-Kaplan’s result.

##### MSC:
 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 14M10 Complete intersections