Zero-cycles on self-products of surfaces: some new examples verifying Voisin's conjecture

TL;DR

This paper presents new examples of surfaces with large geometric genus that support Voisin's conjecture on zero-cycles in self-products, contributing to the understanding of algebraic cycles on surfaces.

Contribution

The authors identify specific surfaces with large geometric genus that verify Voisin's conjecture, providing new evidence and examples in the study of algebraic cycles.

Findings

Surfaces with large p_g verify Voisin's conjecture.

New explicit examples supporting the conjecture.

Enhanced understanding of zero-cycle behavior on surfaces.

Abstract

An old conjecture of Voisin describes how $0$-cycles of a surface $S$ should behave when pulled-back to the self-product $S^m$ for $m>p_g(S)$. We exhibit some surfaces with large $p_g$ that verify Voisin's conjecture.