Half twists and the cohomology of hypersurfaces

Details Half twists and the cohomology of hypersurfaces Half twists and the cohomology of hypersurfaces

2000-08-22

arxiv.org/abs/math/0008170v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight k-1, its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge substructure in the cohomology. We determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces. We use our results to prove the existence of a Kuga-Satake correspondance for certain cubic 4-folds.

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