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arXiv · 2105.04214

Hodge Theory for Polymatroids

Roberto Pagaria·Gian Marco Pezzoli
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Abstract

We construct a Leray model for a discrete polymatroid with arbitrary building set and we prove a generalized Goresky-MacPherson formula. The first row of the model is the Chow ring of the polymatroid; we prove Poincar\'e duality, Hard Lefschetz, and Hodge-Riemann theorems for the Chow ring. Furthermore we provide a relative Lefschetz decomposition with respect to the deletion of an element.

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Roberto Pagaria, Gian Marco Pezzoli. 2021-05-10. Hodge Theory for Polymatroids. https://doi.org/10.1093/imrn%2Frnad001

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