Some cubics with finite-dimensional motive

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.

A family of special cubic fourfolds with motive of abelian type

“…On the other hand, very few examples of cubic fourfolds belonging to the category M Ab rat (C) are known, and they are often related to the Fermat cubic fourfold [19,18,17]. Moreover, it is not clear how the known examples are positioned in the geography of the moduli space.…”