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arXiv · 1712.05983

Algebraic cycles and EPW cubes

Robert Laterveer
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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).

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Robert Laterveer. 2017-12-16. Algebraic cycles and EPW cubes. https://doi.org/10.1002/mana.201600518

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