A semi-small decomposition of the Chow ring of a matroid
A semi-small decomposition of the Chow ring of a matroid
复制标题
DOI：
10.1016/j.aim.2022.108646
复制
发表时间：
2020-02
影响因子：
1.7
通讯作者：
Tom Braden;June Huh;Jacob P. Matherne;N. Proudfoot;Botong Wang
中科院分区：
文献类型：
--
作者：
Tom Braden;June Huh;Jacob P. Matherne;N. Proudfoot;Botong Wang
本文给出拟阵M的Chow环的一个半小正交分解。利用分解给出了Chow环的Poincaré对偶、硬Lefschetz定理和Hodge-Riemann关系的简单证明，恢复了[1]的主要结果.我们还引入了M的增广Chow环，并证明了一个类似的半小正交分解对增广Chow环成立。
We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem, and the Hodge–Riemann relations for the Chow ring, recovering the main result of [1]. We also introduce the augmented Chow ring of M and show that a similar semi-small orthogonal decomposition holds for the augmented Chow ring.