Half twists and the cohomology of hypersurfaces |
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Authors: | B. van Geemen E. Izadi |
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Affiliation: | (1) Dipartimento di Matematica, Università di Pavia, via Ferrata 1, I-27100 Pavia, Italia (e-mail: geemen@dragon.ian.pv.cnr.it) , IT;(2) Department of Mathematics, Boyd Graduate Studies Research Center, University of Georgia, Athens, GA 30602-7403, USA (e-mail: izadi@math.uga.edu) , US |
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Abstract: | A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight , 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 correspondence for certain cubic 4-folds. Received: 25 August 2000; in final form: 8 January 2001 / Published online: 18 January 2002 |
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