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

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

2006-05-17

arxiv.org/abs/math/0605483v1

Proc. Edinb. Math. Soc., 53, 13-29 (2010)

Mathematics

Algebraic Geometry

Scientific paper

10.1017/S001309150700017X

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.

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