A semi-small decomposition of the Chow ring of a matroid

Braden, Tom; Huh, June; Matherne, Jacob P.; Proudfoot, Nicholas; Wang, Botong

doi:10.1016/j.aim.2022.108646

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A semi-small decomposition of the Chow ring of a matroid

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Matherne, Jacob P.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.aim.2022.108646
(Publisher version)

https://doi.org/10.48550/arXiv.2002.03341
(Preprint)

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Citation

Braden, T., Huh, J., Matherne, J. P., Proudfoot, N., & Wang, B. (2022). A semi-small decomposition of the Chow ring of a matroid. Advances in Mathematics, 409: 108646. doi:10.1016/j.aim.2022.108646.

Cite as: https://hdl.handle.net/21.11116/0000-000B-184F-3

Abstract

We give a semi-small orthogonal decomposition of the Chow ring of a matroid
M. The decomposition is used to give simple proofs of Poincar\'e duality, the
hard Lefschetz theorem, and the Hodge-Riemann relations for the Chow ring,
recovering the main result of [AHK18]. We also show that a similar semi-small
orthogonal decomposition holds for the augmented Chow ring of M.