A family of K3 surfaces having finite-dimensional motive

TL;DR

This paper presents a 4-dimensional family of K3 surfaces with finite-dimensional motives and verifies Voisin's conjecture on 0-cycles for these surfaces.

Contribution

It introduces a new family of K3 surfaces with finite-dimensional motives and confirms a conjecture related to 0-cycles on their self-products.

Findings

Verification of Voisin's conjecture for the family

Existence of a 4-dimensional family with finite-dimensional motive

Implications for the study of K3 surfaces' motives

Abstract

This short note contains an example of a 4-dimensional family of K3 surfaces having finite-dimensional motive. Some consequences are presented, for instance the verification of a conjecture of Voisin (concerning 0-cycles on the self-product) for K3 surfaces in this family.