The infinitesimal and generalized Hodge conjecture for some families of sextic threefolds

This paper deals with some families of protective hypersurfaces of degree 6 and dimension 3, left invariant under certain actions of the group of the cubic roots of unity. The general Grothendieck-Hodge conjecture, for the families above and for their intersections, is verified. In particular certain families of elliptic curves on the general element of these families are closely investigated and their degeneration at the Fermat point is studied. These results are used to verify the general Infinitesimal Hodge Conjecture extending to the general type case a similar conjecture due to A. Albano and S. Katz.