Algebraic cycles on hyper-K\"ahler varieties of generalized Kummer type

Author:

Salvatore Floccari, Mauro Varesco

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-08-08 16:00:00

Abstract

We prove the conjectures of Hodge and Tate for any four-dimensional hyper-K\"ahler variety of generalized Kummer type. For an arbitrary variety $X$ of generalized Kummer type, we show that all Hodge classes in the subalgebra of the rational cohomology generated by $H^2(X,\mathbb{Q})$ are algebraic.

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