Variations of Hodge structure, expressed by meromorphic differentials on the projective plane

Abstract

The tautological variations of Hodge structure over Siegel upper half space, the open quadric and the generalized ball are expressed explicitely by the variations of Hodge structure of Weil hypersurfaces in projective spaces. That realizes all the abelian-motivic variations of Hodge structure by families of Jacobians of plane curves, which are known to be described by meromorphic differentials on the projective plane. As a consequence, the geometric origin of a maximal dimensional variation of Hodge structure turns to be sufficient for expressing it by meromorphic differentials on the projective plane.