Hodge Theory for Polymatroids
Algebraic Geometry
2023-10-06 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.2105.04214,
title = {Hodge Theory for Polymatroids},
author = {Roberto Pagaria and Gian Marco Pezzoli},
journal= {arXiv preprint arXiv:2105.04214},
year = {2023}
}
Comments
41 pages, 4 figure. Comments are welcome