Nongenericity of variations of hodge structure for hypersurfaces of high degree

Abstract

In this paper, we are interested in proving that the infinitesimal variations of Hodge structure for hypersurfaces for hypersurfaces of high-enough degree lie in a proper subvariety of the variety of all integral elements of the Griffiths transversality system. That is, this proves that in this case, the geometric infinitesimal variations of Hodge structure satisfy further conditions rather than just being integral elements of the Griffiths system. This is proved using the Jacobian ring representation of the (primitive) cohomology of the hypersurfaces and a space of symmetrizers as defined by Donagi, but here, we use the Jacobian ring representation to identify a geometric structure carried by the variety of all integral elements.