Hodge Theory for Polymatroids

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 Poincaré 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.

41 pages, 4 figure. Comments are welcome

References in corpus (2)

• Matroids are not Ehrhart positive
• Tautological classes of matroids

Cited by in corpus (1)

• Numerical characterization of the hard Lefschetz classes of dimension two, I: supercritical collections under certain rearrangement