Kuga-Satake varieties and the Hodge conjecture
| dc.creator | van Geemen, Bert | |
| dc.date | 1999-03-24 | |
| dc.date.accessioned | 2026-07-07T05:28:27Z | |
| dc.date.available | 2026-07-07T05:28:27Z | |
| dc.description | This 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.description | 23 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.identifier | https://arxiv.org/abs/math/9903146 | |
| dc.identifier | http://arxiv.org/abs/math/9903146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78266 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Kuga-Satake varieties and the Hodge conjecture | |
| dc.type | text |