Algebraic cycles on surfaces with $p_g=1$ and $q=2$

TL;DR

This paper proves Voisin's conjecture regarding zero-cycles on the self-product of certain algebraic surfaces with specific geometric properties, advancing understanding in algebraic geometry.

Contribution

It establishes Voisin's conjecture for surfaces with geometric genus one and irregularity two, a case previously unresolved.

Findings

Voisin's conjecture is confirmed for surfaces with p_g=1 and q=2

Provides new insights into the structure of zero-cycles on these surfaces

Advances the classification of algebraic surfaces with specific invariants

Abstract

This note is about an old conjecture of Voisin, which concerns zero--cycles on the self-product of surfaces of geometric genus one. We prove this conjecture for surfaces with $p_g=1$ and $q=2$.