On the action of symplectic automorphisms on the $C{H}_0$-groups of some hyper-Kähler fourfolds

Abstract

We prove that for any polarized symplectic automorphism of the Fano variety of lines of a cubic fourfold (equipped with the Plücker polarization), the induced action on the Chow group of 0-cycles is identity, as predicted by Bloch-Beilinson conjecture.

26 pages. Final version. To appear in Mathematische Zeitschrift

References in corpus (4)

• Symplectic involutions of K3 surfaces act trivially on CH_0
• A remark on the Torelli theorem for cubic fourfolds
• Symplectic automorphisms of K3 surfaces of arbitrary order
• On the Chow groups of the variety of lines of a cubic fourfold

Cited by in corpus (2)

• Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfolds
• Classification of order sixteen non-symplectic automorphisms on K3 surfaces