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

Abstract

An old conjecture of Voisin describes how zero-cycles on a variety X should behave when pulled-back to the self-product X m for m larger than the geometric genus of X. Using complete intersections of quadrics, we give examples of varieties in any dimension and with arbitrarily high geometric genus that verify Voisin's conjecture.