Zero-cycles on Cancian–Frapporti surfaces

Abstract

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 self-products of varieties: some elementary examples verifying Voisin's conjecture

“…Examples of surfaces of geometric genus 1 verifying the conjecture (or a variant conjecture) are given in [28], [12], [14], [15], [30]. Examples of other varieties verifying the conjecture are given in [28], [18], [13], [16], [17], [19], [2], [20], [27], [5].…”