Algebraic cycles on hyper-Kähler varieties of generalized Kummer type

2025/10/29 by Floccari, Salvatore, Varesco, Mauro
#14C25 #14C30 #14J28 #14J42 #510

paper · doi:10.15488/19878

Abstract

We prove the conjectures of Hodge and Tate for any four-dimensional hyper-Kähler 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 H²(X,Q) are algebraic.

Related

• The Hodge and Tate conjectures for hyper-Kähler sixfolds of generalized Kummer type
• Hodge similarities, algebraic classes, and Kuga-Satake varieties
• Hodge theory, algebraic cycles of hyper-Kähler manifolds
• Algebraic cycles on a generalized Kummer variety
• K3 surfaces associated with varieties of generalized Kummer type