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

TL;DR

This paper provides elementary examples of varieties with high geometric genus that verify Voisin's conjecture on zero-cycles on self-products, expanding the understanding of the conjecture through explicit cases.

Contribution

It introduces new examples of varieties satisfying Voisin's conjecture using complete intersections of quadrics, applicable in any dimension with high geometric genus.

Findings

Examples verify Voisin's conjecture for high-genus varieties

Construction of varieties using complete intersections of quadrics

Verification holds in arbitrary dimensions

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.