# Non-genericity of infinitesimal variations of Hodge structures arising in some geometric contexts

Research paper by Emmanuel Allaud, Javier Fernandez

Indexed on: 17 May '06Published on: 17 May '06Published in: Mathematics - Algebraic Geometry

#### Abstract

We prove that the infinitesimal variations of Hodge structure arising in a number of geometric situations are non-generic. In particular, we consider the case of generic hypersurfaces in complete smooth projective toric varieties, generic hypersurfaces in weighted projective spaces and generic complete intersections in projective space and show that, for sufficiently high degrees, the corresponding infinitesimal variations are non-generic.