On Voisin's conjecture for zero-cycles on hyperkaehler varieties

Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin’s conjecture in the setting of hyperk"ahler varieties, and we prove this reformulated conjecture for one family of hyperk"ahler fourfolds.