Data di Pubblicazione:
2003
Citazione:
Quaternionic pryms and Hodge classes / Bert van Geemen, Alessandro Verra. - In: TOPOLOGY. - ISSN 0040-9383. - 42:1(2003), pp. 35-53.
Abstract:
Abelian varieties of dimension 2n on which a definite quaternion algebra acts are parametrized by symmetrical domains of dimension n(n-1)/2. Such abelian varieties have primitive Hodge classes in the middle dimensional cohomology group. In general, it is not clear that these are cycle classes. In this paper we show that a particular 6-dimensional family of such 8-folds are Prym varieties and we use the method of C. Schoen to show that all Hodge classes on the general abelian variety in this family are algebraic. We also consider Hodge classes on certain 5-dimensional subfamilies and relate these to the Hodge conjecture for abelian 4-folds.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Hodge conjecture, Prym varieties
Elenco autori:
Bert van Geemen, Alessandro Verra
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