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