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arXiv · 2105.02224

Algebraic cycles and intersections of a quadric and a cubic

Robert Laterveer
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Abstract

Let $Y$ be a smooth complete intersection of a quadric and a cubic in $\mathbb{P}^n$, with $n$ 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 the resolution of singularities of a general nodal cubic hypersurface of even dimension.

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Robert Laterveer. 2021-05-05. Algebraic cycles and intersections of a quadric and a cubic. https://arxiv.org/abs/2105.02224

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