On the Chow groups of certain EPW sextics

Abstract

This note is about the Hilbert square X = S [2] , where S is a general K3 surface of degree 10, and the anti-symplectic birational involution ι of X constructed by O'Grady. The main result is that the action of ι on certain pieces of the Chow groups of X is as expected by Bloch's conjecture. Since X is birational to a double EPW sextic X ′ , this has consequences for the Chow ring of the EPW sextic Y ⊂ P 5 associated to X ′ .

Algebraic cycles and EPW cubes

“…Returning to equality (25), this implies that 3 for general b ∈ B , which is exactly statement (23) that we needed to prove. The proof of theorem 4.1 is now complete.…”

“…Then ι * = (−1) i id : A 2i (2i) (X) → A 2i (X) , ι * = (−1) i id : A 2m (2i) (X) → A 2m (X) . This conjecture is studied, and proven in some particular cases, in [22], [24], [23], [25], [26]. The aim of this note is to provide some more examples where conjecture 1.1 is verified, by considering "double EPW cubes" in the sense of [15] (cf.…”

“…This conjecture is studied, and proven in some particular cases, in [21][22][23][24][25]. The aim of this note is to provide some more examples where Conjecture 1.1 is verified, by considering "double EPW cubes" in the sense of [14] (cf.…”

On Chow groups of some hyperkahler fourfolds with a non-symplectic involution, II

“…This conjecture is studied (and proven in some favourable cases) in [14], [15], [16], [17], [18]. The aim of this article is to provide more examples where conjecture 1.1 is verified, by considering Fano varieties of lines on cubic fourfolds.…”

On the Chow groups of some hyperkähler fourfolds with a non-symplectic involution

“…Then ι * = (−1) i id : A 2i (2i) (X) → A 2i (X) , ι * = (−1) i id : A 2m (2i) (X) → A 2m (X) . This conjecture is studied, and proven in some particular cases, in [13], [15], [14], [16]. The aim of this note is to provide some more examples where conjecture 1.1 is verified, by considering Fano varieties of lines on cubic fourfolds.…”