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.
Pagaria R., Pezzoli G.M. (2023). Hodge Theory for Polymatroids. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023(23), 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:
| File | Dimensione | Formato | |
|---|---|---|---|
|
main IMRN.pdf
Open Access dal 03/03/2024
Tipo:
Postprint
Licenza:
Licenza per accesso libero gratuito
Dimensione
577.72 kB
Formato
Adobe PDF
|
577.72 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
