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

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  • René Mboro

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.

Suggested Citation

  • René Mboro, 2025. "A remark on the product by the hyperplane class in the Chow ring of some complete intersections," Mathematische Nachrichten, Wiley Blackwell, vol. 298(6), pages 2014-2036, June.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:6:p:2014-2036
    DOI: 10.1002/mana.202400041
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