The Bergman fan of a polymatroid

Botong Wang; Colin Crowley; Connor Simpson; June Huh; Matt Larson

The Bergman fan of a polymatroid

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arxiv 2207.08764 v2 pith:YANPAWMH submitted 2022-07-18 math.CO math.AG

Colin Crowley , June Huh , Matt Larson , Connor Simpson , Botong Wang This is my paper · ORCID

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keywords bergmanpolymatroidchowringahlerestablishintroduceisomorphic

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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.

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Syzygies of polymatroidal ideals
math.AC 2025-07 conditional novelty 7.0 of 10

For every polymatroid, the cave polynomial is valuative, its support is a generalized polymatroid, and its coefficients are the Möbius values, settling the Bandari-Bayati-Herzog and Castillo-Cid-Ruiz-Mohammadi-Montano...

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