# Algebraic cycles and intersections of three quadrics

Abstract : Let $Y$ be a smooth complete intersection of three quadrics, and assume the dimension of $Y$ is even. We show that $Y$ has a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers of) $Y$ displays K3-like behaviour. As a by-product of the argument, we also establish a multiplicative Chow-K\"unneth decomposition for double planes.
Document type :
Journal articles
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https://hal.archives-ouvertes.fr/hal-03323645
Contributor : robert laterveer Connect in order to contact the contributor
Submitted on : Sunday, August 22, 2021 - 3:13:49 PM
Last modification on : Friday, April 1, 2022 - 3:57:34 AM

### Citation

Robert Laterveer. Algebraic cycles and intersections of three quadrics. Math. Proc. Cambridge Phil. Soc., In press, ⟨10.1017/S030500412100058X⟩. ⟨hal-03323645⟩

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