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.
Surfaces with involution and Prym constructions
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abstract
An involution on a surface induces involutions on the cohomology, the Chow group and the Brauer group of the surface. We give a detailed study of those actions. We show that the odd part of these groups can be used to describe the geometry of cubic fourfolds and conic bundles over $\mathbb{P}^3$.
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math.AG 1years
2022 1verdicts
UNVERDICTED 1representative citing papers
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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.