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

TL;DR

This paper reformulates Voisin's conjecture for zero-cycles on hyperk"ahler varieties and proves it for a specific family of hyperk"ahler fourfolds, advancing understanding in algebraic geometry.

Contribution

It introduces a reformulation of Voisin's conjecture for hyperk"ahler varieties and confirms it for a particular family of fourfolds, providing new evidence.

Findings

Proof of the reformulated conjecture for a family of hyperk"ahler fourfolds

Enhanced understanding of zero-cycles on hyperk"ahler varieties

Progress towards the Bloch-Beilinson conjectures

Abstract

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.