The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and establish some properties of their Chow rings. First, we prove a Beauville–Voisin type theorem for zero-cycles on double EPW sextics; precisely, we show that the codimension-4 part of the subring of the Chow ring of a double EPW sextic generated by divisors, the Chern classes and codimension-2 cycles invariant under the anti-symplectic covering involution has rank one. Second, for double EPW sextics birational to the Hilbert square of a K3 surface, we show that the action of the anti-symplectic involution on the Chow group of zero-cycles commutes with the Fourier decomposition of Shen–Vial.

中文翻译：

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双 EPW 六分法上的零周期

hyperKähler 变种的 Chow 环被推测具有特别丰富的结构。在本文中，我们关注局部完整的双 EPW 六色系，并建立了它们 Chow 环的一些性质。首先，我们证明了双 EPW 六线谱上零周期的 Beauville-Voisin 型定理；确切地说，我们证明了在反辛覆盖对合下由除数、陈类和 codimension-2 循环不变量生成的双 EPW 六分仪的 Chow 环的子环的 codimension-4 部分具有秩 1。其次，对于与 K3 表面的希尔伯特平方双有理的双 EPW 六分频，我们证明了反辛对合对零循环 Chow 群的作用与 Shen-Vial 的傅里叶分解对易。