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arXiv · 2502.12010

Hyperplane arrangements and the Gauss map of a pencil

Thiago Fassarella·Nivaldo Medeiros
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Abstract

We show that the coefficients of the characteristic polynomial of a central hyperplane arrangement $\mathcal A$, coincide with the multidegrees of the Gauss map of a pencil of hypersurfaces naturally associated to $\mathcal A$. As a consequence, we obtain a proof of the Heron-Rota-Welsh conjecture for matroids representable over a field of characteristic zero.

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Thiago Fassarella, Nivaldo Medeiros. 2025-02-17. Hyperplane arrangements and the Gauss map of a pencil. https://arxiv.org/abs/2502.12010

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