@article{59f19385c11f4c1a87a5910545eef4c5,
title = "A semi-small decomposition of the Chow ring of a matroid",
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 [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.",
keywords = "Chow rings, Decomposition theorem, K{\"a}hler package, Matroids, Semi-small maps",
author = "Tom Braden and June Huh and Matherne, {Jacob P.} and Nicholas Proudfoot and Botong Wang",
note = "Funding Information: June Huh received support from NSF Grant DMS-1638352 and the Ellentuck Fund . Jacob Matherne received support from NSF Grant DMS-1638352 , the Association of Members of the Institute for Advanced Study , the Max Planck Institute for Mathematics in Bonn, and the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy - GZ 2047/1, Projekt-ID 390685813 . Nicholas Proudfoot received support from NSF Grants DMS-1565036 , DMS-1954050 , and DMS-2039316 . Botong Wang received support from NSF Grant DMS-1701305 and the Alfred P. Sloan Foundation . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2022",
month = nov,
day = "19",
doi = "10.1016/j.aim.2022.108646",
language = "English (US)",
volume = "409",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}