Hard Lefschetz for Chow groups of generalized Kummer varieties

The main result of this note is a hard Lefschetz theorem for the Chow groups of generalized Kummer varieties. The same argument also proves hard Lefschetz for Chow groups of Hilbert schemes of abelian surfaces. As a consequence, we obtain new information about certain pieces of the Chow groups of generalized Kummer varieties, and Hilbert schemes of abelian surfaces. The proofs are based on work of Shen-Vial and Fu-Tian-Vial on multiplicative Chow-Künneth decompositions.

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