Hyperplane arrangements and the Gauss map of a pencil
Algebraic Geometry
2025-06-05 v2 Combinatorics
Abstract
We show that the coefficients of the characteristic polynomial of a central hyperplane arrangement , coincide with the multidegrees of the Gauss map of a pencil of hypersurfaces naturally associated to . As a consequence, we obtain a proof of the Heron-Rota-Welsh conjecture for matroids representable over a field of characteristic zero.
Keywords
Cite
@article{arxiv.2502.12010,
title = {Hyperplane arrangements and the Gauss map of a pencil},
author = {Thiago Fassarella and Nivaldo Medeiros},
journal= {arXiv preprint arXiv:2502.12010},
year = {2025}
}