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

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-10-09 DOI:10.1002/mana.202400041

René Mboro

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引用次数: 0

Abstract

By classical calculation, for a smooth hypersurface $Y \subset P_{C}^{n + 1}$ , the product by the hyperplane class is zero on homologically trivial rational cycles, that is, $\cdot H_{| Y} : {CH}_{i} {(Y)}_{hom, Q} \to {CH}_{i - 1} {(Y)}_{hom, Q}$ is 0 for any $i$ . This note extends that result to some complete intersections.

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一些完全交点的Chow环上超平面类积的注解

通过经典计算，对于光滑超曲面Y∧P C n+1 $Y\子集\mathbb {P}^{n+1}_{\mathbb {C}}$，该超平面类在同调平凡有理环上的积为零，即：·h b| y：何志强，Q→CH i−1 (Y) hm，Q $\cdot H_{|Y}:{\rm CH}_i(Y)_{\text{home},\mathbb {Q}}\rightarrow {\rm CH}_{i-1}(Y)_{\text{home},\mathbb {Q}}$对于任何i$ i$都是0。本文将该结果扩展到一些完整的交叉点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index