Crowley, Huh, Larson, Simpson, Wang — The Bergman Fan Of A Polymatroid (2024)

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Colin Crowley, June Huh, Matt Larson, Connor Simpson, Botong Wang. The Bergman Fan of a Polymatroid. arXiv. 2024.

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Abstract

We introduce the Bergman fan of a polymatroid and prove that the Chow ring of the Bergman fan is isomorphic to the Chow ring of the polymatroid. Using the Bergman fan, we establish the K\"ahler package for the Chow ring of the polymatroid, recovering and strengthening a result of Pagaria–Pezzoli.