Surfaces of lines in cubic fourfolds intersecting a fixed line admit a motivic splitting with one K3-like component; an analogue of the Beauville-Voisin class is defined and the push-forward to the Fano variety is studied via the Bloch-Beilinson filtration splitting of Shen-Vial.
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Chow groups of surfaces of lines in cubic fourfolds
Surfaces of lines in cubic fourfolds intersecting a fixed line admit a motivic splitting with one K3-like component; an analogue of the Beauville-Voisin class is defined and the push-forward to the Fano variety is studied via the Bloch-Beilinson filtration splitting of Shen-Vial.