Some cubics with finite-dimensional motive

TL;DR

This paper introduces a family of high-dimensional cubic varieties with finite-dimensional motives and verifies related conjectures, advancing understanding in algebraic geometry and motive theory.

Contribution

It constructs new examples of cubics with finite-dimensional motives and confirms conjectures of Voevodsky and Murre for these cases.

Findings

Verified Voevodsky's conjecture for these cubics

Confirmed Murre's conjecture for their Fano varieties

Established finite-dimensionality of motives in these examples

Abstract

This small note presents in any dimension a family of cubics that have finite-dimensional motive (in the sense of Kimura). As an illustration, we verify a conjecture of Voevodsky for these cubics, and a conjecture of Murre for the Fano variety of lines of these cubics.