Chow groups of surfaces of lines in cubic fourfolds

TL;DR

This paper studies the motivic decomposition of the surface of lines in cubic fourfolds, defining an analogue of the Beauville-Voisin class and analyzing the push-forward map within the Bloch-Beilinson filtration.

Contribution

It introduces a motivic splitting for the surface of lines in cubic fourfolds and defines a Beauville-Voisin type class in this context.

Findings

Surface of lines splits motivically into two parts, one resembling a K3 surface.

Defined an analogue of the Beauville-Voisin class for this surface.

Analyzed the push-forward map to the Fano variety within the Bloch-Beilinson filtration.

Abstract

The surface of lines in a cubic fourfold intersecting a fixed line splits motivically into two parts, one of which resembles a K3 surface. We define the analogue of the Beauville-Voisin class and study the push-forward map to the Fano variety of all lines with respect to the natural splitting of the Bloch-Beilinson filtration introduced by Mingmin Shen and Charles Vial.