Hypersurface variations are maximal. I (Q1100244)

A variation of Hodge structure over a connected complex manifold U is called maximal if the image of the associated period mapping \(v: U\to \Gamma \setminus D\) is not contained in the image of another such period mapping of strictly larger dimension. The main result is, that the variation of Hodge structure associated to the natural family of smooth projective hypersurfaces of given degree and dimension is maximal as soon as its Hodge level \(\max \{p-q| h^{p,q}\neq 0\}>1\).