Some elementary examples of quartics with finite-dimensional motive

TL;DR

This paper presents simple examples of quartic hypersurfaces with finite-dimensional motives and verifies Voevodsky's conjecture on smash-equivalence for some of these cases.

Contribution

It provides elementary examples of quartics with finite-dimensional motives and confirms Voevodsky's conjecture in specific instances.

Findings

Identified quartic hypersurfaces with finite-dimensional motives

Verified Voevodsky's smash-equivalence conjecture for certain quartics

Contributed to understanding motives of algebraic varieties

Abstract

This small note contains some easy examples of quartic hypersurfaces that have finite-dimensional motive. As an illustration, we verify a conjecture of Voevodsky (concerning smash-equivalence) for some of these special quartics.