Hodge classes on abelian varieties of low dimension

B. J. J. Moonen; Yu. G. Zarhin

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arXiv · math/9901113

Hodge classes on abelian varieties of low dimension

B. J. J. Moonen·Yu. G. Zarhin

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Abstract

In this paper we study Hodge classes on complex abelian varieties. We prove some general results that allow us, in certain cases, to compute the Hodge group of a product abelian variety $X = X_1 \times X_2$ once we know the Hodge groups of the two factors. Using these results we can compute the Hodge groups of all abelian varieties of dimension $\leq 5$. We prove that the Hodge ring of any such abelian variety $X$ is generated by divisor classes together with the so-called Weil classes on (quotients of) $X$.

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B. J. J. Moonen, Yu. G. Zarhin. 1999-04-13. Hodge classes on abelian varieties of low dimension. https://arxiv.org/abs/math/9901113

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