Abstract
Let X be a hyperkahler variety, and let G be a group of finite order non-symplectic automorphisms of X. Beauville’s conjectural splitting property predicts that each Chow group of X should split in a finite number of pieces. The Bloch–Beilinson conjectures predict how G should act on these pieces of the Chow groups: certain pieces should be invariant under G, while certain other pieces should not contain any non-trivial G-invariant cycle. We can prove this for two pieces of the Chow groups when X is the Hilbert scheme of a K3 surface and G consists of natural automorphisms. This has consequences for the Chow ring of the quotient X/G.
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