Algebraic cycles on Fano varieties of some cubics

TL;DR

This paper investigates the cycle-theoretic properties of Fano varieties of lines on smooth cubic fivefolds, leveraging their finite-dimensional motives, and extends some results to related Fano varieties in other dimensions.

Contribution

It demonstrates that the Fano variety of lines on a smooth cubic fivefold has finite-dimensional motive and explores Chow groups of similar Fano varieties in different dimensions.

Findings

Fano variety of lines on cubic fivefold has finite-dimensional motive

Results on Chow groups of Fano varieties in other dimensions

Cycle-theoretic properties linked to motive finiteness

Abstract

This note is about cycle-theoretic properties of the Fano variety of lines on a smooth cubic fivefold. The arguments are based on the fact that this Fano variety has finite-dimensional motive. We also present some results concerning Chow groups of Fano varieties of lines on certain cubics in other dimensions.