Algebraic cycles on the Fano variety of lines of a cubic fourfold

Abstract

In this text we prove that if a smooth cubic in $\PR^5$ has its Fano variety of lines birational to the Hilbert scheme of two points on a K3 surface, then there exists a smooth projective curve or a smooth projective surface embedded in the Fano variety, such that the kernel of the push-forward (at the level of zero cycles ) induced by the closed embedding is torsion.

arXiv comment13 pages

Cited by in corpus (2)

• On the rationality and the finite dimensionality of a cubic fourfold
• Mumford-Roitman argument on families