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 Poincare 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.
Hodge Theory for Polymatroids / Pagaria R.; Pezzoli G.M.. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2023:23(2023), pp. 20118-20168. [10.1093/imrn/rnad001]
Hodge Theory for Polymatroids
Pagaria R.
;Pezzoli G. M.
2023
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 Poincare 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.File in questo prodotto:
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