Abstract
In this paper for every p > 0 the universal family of the hypersurfaces of degree 2 p and dimension 3 invariant under a certain action of the group of p-th roots of unity is considered. The maximal abelian rational sub-Hodge structure of weight 3 is investigated on the general element and the general Grothendieck-Hodge conjecture is checked for the general point of some special sub-families.
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