Half Twists and the Cohomology of Hypersurfaces
نویسنده
چکیده
A Hodge structure V of weight k on which a CM eld acts de nes, 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 de nes an action of a cyclotomic eld 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 correspondence for certain cubic 4-folds.
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