Algebraic cycles on genus-2 modular fourfolds

Arapura, Donu

doi:10.2140/ant.2019.13.211

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Algebraic cycles on genus-2 modular fourfolds

Donu Arapura

Vol. 13 (2019), No. 1, 211–225

DOI: 10.2140/ant.2019.13.211

Abstract

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 $ℂ$ under projection to the moduli space of curves. Using this, it shown that the Hodge and Tate conjectures hold for these varieties.

Keywords

Hodge conjecture, Tate conjecture, moduli of curves

Mathematical Subject Classification 2010

Primary: 14C25

Milestones

Received: 28 February 2018

Revised: 11 November 2018

Accepted: 30 November 2018

Published: 13 February 2019

Authors

Donu Arapura
Department of Mathematics Purdue University West Lafayette, IN United States

Vol. 13, No. 1, 2019