A family of cubic fourfolds with finite-dimensional motive

TL;DR

This paper proves that a specific 10-dimensional family of cubic fourfolds has finite-dimensional motive using algebraic correspondences and spread techniques, with implications for algebraic geometry.

Contribution

It introduces a new proof that certain cubic fourfolds have finite-dimensional motive by combining Kuga-Satake correspondence with Voisin's spread method.

Findings

Finite-dimensional motive established for a 10-dimensional family of cubic fourfolds.

Application of algebraic Kuga-Satake correspondence to cubic fourfolds.

Implications for the structure and classification of algebraic varieties.

Abstract

We prove that cubic fourfolds in a certain 10-dimensional family have finite-dimensional motive. The proof is based on the van Geemen-Izadi construction of an algebraic Kuga-Satake correspondence for these cubic fourfolds, combined with Voisin's method of "spread". Some consequences are given.