Algebraic cycles and EPW cubes

Abstract

Let $X$ be a hyperkähler variety with an anti-symplectic involution $\iota$. 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 $\iota$ 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 $X/\iota$, which is an "EPW cube" (in the sense of Iliev-Kapustka-Kapustka-Ranestad).

32 pages, to appear in Math. Nachrichten, feedback welcome

References in corpus (2)

• The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II
• Hard Lefschetz for Chow groups of generalized Kummer varieties