A remark on the product by the hyperplane class in the Chow ring of some complete intersections

René Mboro

Mathematische Nachrichten, 2025, vol. 298, issue 6, 2014-2036

Abstract: By classical calculation, for a smooth hypersurface Y⊂PCn+1$Y\subset \mathbb {P}^{n+1}_{\mathbb {C}}$, the product by the hyperplane class is zero on homologically trivial rational cycles, that is, ·H|Y:CHi(Y)hom,Q→CHi−1(Y)hom,Q$\cdot H_{|Y}:{\rm CH}_i(Y)_{\text{hom},\mathbb {Q}}\rightarrow {\rm CH}_{i-1}(Y)_{\text{hom},\mathbb {Q}}$ is 0 for any i$i$. This note extends that result to some complete intersections.

Date: 2025
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