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arXiv · 2512.06430

Questions on the Chow ring of complete intersections

Robert Laterveer
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Abstract

We state several questions, and prove some partial results, about the Chow ring $A^\ast(X)$ of complete intersections in projective space. For one thing, we prove that if $X$ is a general Calabi-Yau hypersurface, the intersection product $A^2(X)\cdot A^i(X)$ is one-dimensional, for any $i>0$. We also show that quintic threefolds have a multiplicative Chow-K\"unneth (MCK) decomposition. We wonder whether all Calabi-Yau hypersurfaces might have an MCK decomposition, and prove this is the case conditional to a conjecture of Voisin.

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Robert Laterveer. 2025-12-06. Questions on the Chow ring of complete intersections. https://arxiv.org/abs/2512.06430

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