# Algebraic cycles and intersections of 2 quadrics

Abstract : A smooth intersection $Y$ of two quadrics in $\mathbb{P}^{2g+1}$ has Hodge level 1. We show that such varieties $Y$ have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of $Y$ injects into cohomology.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-03223474
Contributor : robert laterveer Connect in order to contact the contributor
Submitted on : Tuesday, May 11, 2021 - 8:50:39 AM
Last modification on : Friday, April 1, 2022 - 3:50:32 AM

### Citation

Robert Laterveer. Algebraic cycles and intersections of 2 quadrics. Mediterranean Journal of Mathematics, Springer Verlag, In press, ⟨10.1007/s00009-021-01787-5⟩. ⟨hal-03223474⟩

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