# Algebraic cycles and Lehn-Lehn-Sorger-van Straten eightfolds

Abstract : This article is about Lehn-Lehn-Sorger-van Straten eightfolds $Z$, and their anti-symplectic involution $\iota$. When $Z$ is birational to the Hilbert scheme of points on a K3 surface, we give an explicit formula for the action of $\iota$ on the Chow group of $0$-cycles of $Z$. The formula is in agreement with the Bloch-Beilinson conjectures, and has some non-trivial consequences for the Chow ring of the quotient.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-03341880
Contributor : Robert Laterveer <>
Submitted on : Monday, September 13, 2021 - 8:54:06 AM
Last modification on : Tuesday, September 14, 2021 - 8:44:36 AM

### Identifiers

• HAL Id : hal-03341880, version 1
• ARXIV : 2109.04942

### Citation

Robert Laterveer. Algebraic cycles and Lehn-Lehn-Sorger-van Straten eightfolds. Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP), In press. ⟨hal-03341880⟩

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