Discrete tomography and the Hodge conjecture for certain abelian varieties of CM-type

Abstract

We study a problem in discrete tomography on $\mathbf{Z}^{n}$, and show that there is an intimate connection between the problem and the study of the Hodge cycles on abelian varieties of CM-type. This connection enables us to apply our results in tomography to obtain several infinite families of abelian varieties for which the Hodge conjecture holds.