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Discrete tomography and the Hodge conjecture for certain abelian varieties of CM-type. (English) Zbl 1106.14004

Summary: We study a problem in discrete tomography on \(\mathbb Z^n\), 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.

MSC:

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14K05 Algebraic theory of abelian varieties
39A10 Additive difference equations
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References:

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