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Algebraic cycles and EPW cubes

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  • Robert Laterveer

Abstract

Let 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 X/ι, which is an “EPW cube†(in the sense of Iliev–Kapustka–Kapustka–Ranestad).

Suggested Citation

  • Robert Laterveer, 2018. "Algebraic cycles and EPW cubes," Mathematische Nachrichten, Wiley Blackwell, vol. 291(7), pages 1088-1113, May.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:7:p:1088-1113
    DOI: 10.1002/mana.201600518
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