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arXiv · 1802.09496

Algebraic cycles on genus two modular fourfolds

Donu Arapura
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Abstract

We study universal families of stable genus two curves with level structure. Among other things, it is shown that the (1,1) part is spanned by divisor classes, and that there are no cycles of type (2,2) in the third cohomology of the first direct image. Using this, we deduce the Hodge and Tate conjectures hold for these varieties.

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Donu Arapura. 2018-12-04. Algebraic cycles on genus two modular fourfolds. https://doi.org/10.2140/ant.2019.13.211

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