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The period map and the discriminant. (English. Russian original) Zbl 0684.14001

Math. USSR, Sb. 62, No. 1, 65-81 (1989); translation from Mat. Sb., Nov. Ser. 134(176), No. 1(9), 66-81 (1987).
The base space of a versal deformation of an isolated hypersurface singularity has topological stratification by the Milnor numbers of the singularities occurring in each fibre. On each stratum a period mapping can be defined into the middle dimensional cohomology of a typical fibre. This cohomology can be foliated by the affine translates of a suitable piece of the weight filtration. The inverse image under the period mapping of this foliation is the weight foliation on the stratum of the base. Via the period mapping the intersection form induces a 2-form on the tangent bundle of the foliation. The author is able to show that the period mapping is nondegenerate if the singularities occuring are not too complicated. The weight foliation is computed for the curve singularity \(A_ 4\).
Reviewer: J.Scherk

MSC:

14B07 Deformations of singularities
32S05 Local complex singularities
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
32G20 Period matrices, variation of Hodge structure; degenerations
14J17 Singularities of surfaces or higher-dimensional varieties
14H20 Singularities of curves, local rings
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