Some results on a conjecture of Voisin for surfaces of geometric genus one

TL;DR

This paper provides new examples of surfaces with geometric genus one where Voisin's conjecture on 0-cycles is verified, advancing understanding of the conjecture's validity.

Contribution

It introduces novel examples of surfaces confirming Voisin's conjecture, contributing to the study of 0-cycles on varieties of geometric genus one.

Findings

Verification of Voisin's conjecture for new surface examples

Enhanced understanding of 0-cycle behavior on specific surfaces

Progress towards validating the conjecture in broader cases

Abstract

Inspired by the Bloch-Beilinson conjectures, Voisin has formulated a conjecture concerning the behaviour of 0-cycles on self-products of varieties of geometric genus one. This note presents some new examples of surfaces for which Voisin's conjecture is verified.