Hodge theory for polymatroids

Date: 2022-05-31

Time: 14:45 - 15:45


Roberto Pagaria


Polymatroids are combinatorial objects that generalize matroids, subspace arrangements, and hypergraphs.
In the case of subspace arrangements, De Concini and Procesi constructed a wonderful model and studied the Leray model associated with it.
Adiprasito, Huh, and Katz defined a Chow ring for matroids and used it to prove the log-concavity conjecture.

We provide a Leray model and a Chow ring for polymatroids, which we use to generalize the Goresky-MacPhearson formula to the non-realizable setting.
We also prove that the Chow ring of a polymatroid satisfies Poincaré duality and, on a certain cone, hard Lefschetz theorem and Hodge Riemann bilinear relations.

This is a joint work with Gian Marco Pezzoli.