Quaternionic pryms and Hodge classes
Abstract
Abelian varieties of dimension 2n on which a definite quaternion algebra acts are parametrized by symmetrical domains of dimension n(n1)/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 6dimensional family of such 8folds 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 5dimensional subfamilies and relate these to the Hodge conjecture for abelian 4folds.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103111
 Bibcode:
 2001math......3111V
 Keywords:

 Algebraic Geometry
 EPrint:
 18 pages, LaTeX