Kuga-Satake varieties and the Hodge conjecture

dc.creatorvan Geemen, Bert
dc.date1999-03-24
dc.date.accessioned2026-07-07T05:28:27Z
dc.date.available2026-07-07T05:28:27Z
dc.descriptionThis paper gives an introduction to Kuga-Satake varieties and discusses some aspects of the Hodge conjecture related to them. Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We give a detailed account of the construction of Kuga-Satake varieties and of their decomposition in simple subvarieties. We recall the Hodge conjecture and we point out a connection between the Hodge conjecture for abelian fourfolds and Kuga-Satake varieties. We discuss the implications of the Hodge conjecture on the geometry of surfaces whose second cohomology group has a Kuga-Satake variety. We conclude with some recent results on Kuga-Satake varieties of Hodge structures on which an imaginary quadratic field acts.
dc.description23 pages LaTeX. To appear in: The Arithmetic and Geometry of Algebraic Cycles. Eds. J. Lewis et al. (Proceedings of the NATO ASI and CRM Summer School in Banff, 1998)
dc.identifierhttps://arxiv.org/abs/math/9903146
dc.identifierhttp://arxiv.org/abs/math/9903146
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78266
dc.subjectAlgebraic Geometry
dc.titleKuga-Satake varieties and the Hodge conjecture
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