Algebraic cycles and EPW cubes
Copyright policy )Algebraic cycles and EPW cubes
AbstractLet X be a hyperkähler variety with an anti‐symplectic involution ι. According to Beauville's conjectural “splitting property”, the Chow groups of X should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch–Beilinson conjectures predict how ι should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a 19‐dimensional family of hyperkähler sixfolds that are “double EPW cubes” (in the sense of Iliev–Kapustka–Kapustka–Ranestad). This has interesting consequences for the Chow ring of the quotient , which is an “EPW cube” (in the sense of Iliev–Kapustka–Kapustka–Ranestad).
non-symplectic involution, hyperkähler varieties, Algebraic cycles, (double) EPW cubes, algebraic cycles, Bloch-Beilinson filtration, \(K3\) surfaces, Mathematics - Algebraic Geometry, splitting property, motives, (Equivariant) Chow groups and rings; motives, Bloch's conjecture, Transcendental methods, Hodge theory (algebro-geometric aspects), FOS: Mathematics, 14C15, 14C25, 14C30, multiplicative Chow-Künneth decomposition, Chow groups, Algebraic Geometry (math.AG)
non-symplectic involution, hyperkähler varieties, Algebraic cycles, (double) EPW cubes, algebraic cycles, Bloch-Beilinson filtration, \(K3\) surfaces, Mathematics - Algebraic Geometry, splitting property, motives, (Equivariant) Chow groups and rings; motives, Bloch's conjecture, Transcendental methods, Hodge theory (algebro-geometric aspects), FOS: Mathematics, 14C15, 14C25, 14C30, multiplicative Chow-Künneth decomposition, Chow groups, Algebraic Geometry (math.AG)
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