Discrete tomography and Hodge cycles

Abstract

We study a problem in discrete tomography on the free abelian group of rank $n$ through the theory of distributions on the $n$-dimensional torus, 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 hold.