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arXiv · 2002.03341

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

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

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Tom Braden, June Huh, Jacob P. Matherne, Nicholas Proudfoot, Botong Wang. 2020-02-09. A semi-small decomposition of the Chow ring of a matroid. https://arxiv.org/abs/2002.03341

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