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On Chow groups of some hyperkähler fourfolds with a non-symplectic involution. II. (English) Zbl 1402.14008
Summary: This note is about hyperkähler fourfolds \(X\) admitting a non-symplectic involution \(\iota\). The Bloch-Beilinson conjectures predict the way \(\iota\) should act on certain pieces of the Chow groups of \(X\). The main result of this note is a verification of this prediction for Fano varieties of lines on certain cubic fourfolds. This has some interesting consequences for the Chow ring of the quotient \(X/\iota\).
For Part I see [the author, Int. J. Math. 28, No. 3, Article ID 1750014, 19 p. (2017; Zbl 1397.14010)].
MSC:
14C15 (Equivariant) Chow groups and rings; motives
14C25 Algebraic cycles
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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