We consider a 10-dimensional family of Lehn–Lehn–Sorger–van Straten hyperkähler eightfolds, which have a non-symplectic automorphism of order 3. Using the theory of finite-dimensional motives, we show that the action of this automorphism on the Chow group of 0-cycles is as predicted by the Bloch–Beilinson conjectures. We prove a similar statement for the anti-symplectic involution on varieties in this family. This has interesting consequences for the intersection product of the Chow ring of these varieties.

中文翻译：

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在某些 LEHN-LEHN-SORGER-VAN STRATEN 八折的周环上

我们考虑 Lehn-Lehn-Sorger-van Straten hyperkähler 八倍的 10 维族，它具有 3 阶非辛自同构。使用有限维动机理论，我们证明了这种自同构对 Chow 的作用Bloch-Beilinson 猜想预测的 0 循环组。我们证明了这个家族中变体的反辛对合的类似陈述。这对这些品种的 Chow 环的交集产生了有趣的结果。