Vol. 13, No. 1, 2019

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Algebraic cycles on genus-2 modular fourfolds

Donu Arapura

Vol. 13 (2019), No. 1, 211–225

This paper studies universal families of stable genus-2 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 of under projection to the moduli space of curves. Using this, it shown that the Hodge and Tate conjectures hold for these varieties.

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Hodge conjecture, Tate conjecture, moduli of curves
Mathematical Subject Classification 2010
Primary: 14C25
Received: 28 February 2018
Revised: 11 November 2018
Accepted: 30 November 2018
Published: 13 February 2019
Donu Arapura
Department of Mathematics
Purdue University
West Lafayette, IN
United States