English

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 A\mathcal A, coincide with the multidegrees of the Gauss map of a pencil of hypersurfaces naturally associated to A\mathcal A. 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}
}