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.

An old conjecture of Voisin describes how 0-cycles of a surface S should behave when pulled-back to the self-product $$S^m$$
 for $$m>p_g(S)$$
 . We exhibit some surfaces with large $$p_g$$
 that verify Voisin’s conjecture.

Additional excerpts

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

Zero-cycles on self-products of surfaces: some new examples verifying Voisin’s conjecture

An old conjecture of Voisin describes how 0-cycles on a surface S should behave when pulled-back to the self-product $S^m$ for $m>p_g(S)$. We show that Voisin’s conjecture is true for a 3-dimensional family of surfaces of general type with $p_g=q=2$ and $K^2=7$ constructed by Cancian and Frapporti, and revisited by Pignatelli–Polizzi.

Zero-cycles on Cancian–Frapporti surfaces

background

Algebraic cycles and very special cubic fourfolds

An old conjecture of Voisin describes how $0$-cycles of a surface $S$ should behave when pulled-back to the self-product $S^m$ for $m>p_g(S)$. We exhibit some surfaces with large $p_g$ that verify Voisin's conjecture.

Zero-cycles on self-products of surfaces: some new examples verifying Voisin's conjecture

An old conjecture of Voisin describes how $0$-cycles on a surface $S$ should behave when pulled-back to the self-product $S^m$ for $m>p_g(S)$. We show that Voisin's conjecture is true for a $3$-dimensional family of surfaces of general type with $p_g=q=2$ and $K^2=7$ constructed by Cancian and Frapporti, and revisited by Pignatelli-Polizzi.

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

Citations

Zero-cycles on self-products of surfaces: some new examples verifying Voisin’s conjecture

Zero-cycles on Cancian–Frapporti surfaces

Algebraic cycles and very special cubic fourfolds

Zero-cycles on self-products of surfaces: some new examples verifying Voisin's conjecture

Zero-cycles on Cancian-Frapporti surfaces

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