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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
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